fractional quantum hall effect pdf

The Hall conductivity is thus widely used as a standardized unit for resistivity. Stimulated by tensor networks, we propose a scheme of constructing the few-body models that can be easily accessed by theoretical or experimental means, to accurately capture the ground-state properties of infinite many-body systems in higher dimensions. Its driving force is the reduc-tion of Coulomb interaction between the like-charged electrons. The results suggest that a transition from We show that a linear term coupling the atoms of an ultracold binary mixture provides a simple method to induce an effective and tunable population imbalance between them. <> This effect, termed the fractional quantum Hall effect (FQHE), represents an example of emergent behavior in which electron interactions give rise to collective excitations with properties fundamentally distinct from the fractal IQHE states. The experimental discovery of the fractional quantum Hall effect (FQHE) at the end of 1981 by Tsui, Stormer and Gossard was absolutely unexpected since, at this time, no theoretical work existed that could predict new struc tures in the magnetotransport coefficients under conditions representing the extreme quantum limit. Rev. We propose a standard time-of-flight experiment as a method to observe the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) 4. ratio the lling factor . M uch is understood about the frac-tiona l quantum H all effect. This way of controlling the chemical potentials applies for both bosonic and fermionic atoms and it allows also for spatially and temporally dependent imbalances. Recent achievements in this direction, together with the possibility of tuning interparticle interactions, suggest that strongly correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. At the lowest temperatures (T∼0.5K), the Hall resistance is quantized to values ρ{variant}xy = h/( 1 3 e2) and ρ{variant}xy = h/( 2 3 e2). Moreover, we discuss how these quantized dissipative responses can be probed locally, both in the bulk and at the boundaries of the quantum Hall system. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. linearity above 18 T and exhibited no additional features for filling ]��$�9Y�� C[�>�2RǊ{l5�S��w�o� $${\phi _{n,m}}(\overrightarrow r ) = \frac{{{e^{|Z{|^2}/4{l^2}}}}}{{\sqrt {2\pi } }}{G^{m,n}}(iZ/l)$$ (2) This observation, unexpected from current theoretical models for the quantized Hall effect, suggests the formation of a new electronic state at fractional level occupation. We shall see that the fractional quantum Hall state can be considered as a Bose-condensed state of bosonized electrons. The fact that something special happens along the edge of a quantum Hall system can be seen even classically. However, in the former we need a gap that appears as a consequence of the mutual Coulomb interaction between electrons. Next, we consider changing the statistics of the electrons. The quasiparticles for these ground states are also investigated, and existence of those with charge ± e/5 at nu{=}2/5 is shown. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Strikingly, the Hall resistivity almost reaches the quantized value at a temperature where the exact quantization is normally disrupted by thermal fluctuations. • Fractional quantum Hall effect (FQHE) • Composite fermion (CF) • Spherical geometry and Dirac magnetic monopole • Quantum phases of composite fermions: Fermi sea, superconductor, and Wigner crystal . The reduced density matrix of the ground state is then optimally approximated with that of the finite effective Hamiltonian by tracing over all the "entanglement bath" degrees of freedom. By these methods, it can be shown that the wave function proposed by Laughlin captures the essence of the FQHE. ��-��D?N��q��Tc About this book. Our results demonstrate a new means of effecting dynamical control of topology by manipulating bulk conduction using light. Excitation energies of quasiparticles decrease as the magnetic field decreases. It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Analytical expressions for the degenerate ground state manifold, ground state energies, and gapless nematic modes are given in compact forms with the input interaction and the corresponding ground state structure factors. confirmed. The ground state energy of two-dimensional electrons under a strong magnetic field is calculated in the authors' many-body theory for the fractional quantised Hall effect, and the result is lower than the result of Laughlin's wavefunction. Quantization of the Hall resistance ρ{variant}xx and the approach of a zero-resistance state in ρ{variant}xx are observed at fractional filling of Landau levels in the magneto-transport of the two-dimensional electrons in GaAs(AlGa) As heterostructures. The basic principle is to transform the Hamiltonian on an infinite lattice to an effective one of a finite-size cluster embedded in an "entanglement bath". This effect is explained successfully by a discovery of a new liquid type ground state. The activation energy Δ of ϱxx is maximum at the center of the Hall plateau, when , and decreases on either side of it, as ν moves away from . a plateau in the Hall resistance, is observed in two-dimensional electron gases in high magnetic fields only when the mobile charged excitations have a gap in their excitation spectrum, so the system is incompressible (in the absence of disorder). Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan . It is found that the ground state is not a Wigner crystal but a liquid-like state. The Hall conductivity takes plateau values, σxy =(p/q) e2/h, around ν=p/q, where p and q are integers, ν=nh/eB is the filling factor of Landau levels, n is the electron density and B is the strength of the magnetic field. � �y�)�l�d,�k��4|\�3%Uk��g;g��CK��H�Sre��,Q��L"ׁ}�r3��H:>��kf�5 �xW�� The electron localization is realized by the long-range potential fluctuations, which are a unique and inherent feature of quantum Hall systems. This is not the way things are supposed to … Non-Abelian Fractional Quantum Hall Effect for Fault-Resistant Topological Quantum Computation W. Pan, M. Thalakulam, X. Shi, M. Crawford, E. Nielsen, and J.G. The Fractional Quantum Hall Effect presents a general survery of most of the theoretical work on the subject and briefly reviews the experimental results on the excitation gap. The statistics of a particle can be. changed by attaching a fictitious magnetic flux to the particle. In parallel to the development of schemes that would allow for the stabilization of strongly correlated topological states in cold atoms [1][2][3][21][22][23][24][25][26][27], an open question still remains: are there unambiguous probes for topological order that are applicable to interacting atomic systems? The dissipative response of a quantum system upon a time-dependent drive can be exploited as a probe of its geometric and topological properties. factors below 15 down to 111. Quasi-Holes and Quasi-Particles. Although the nature of the ground state is still not clear, the magnitude of the cusp is consistent with the experimentally observed anomaly in σxy and σxx at 13 filling by Tsui, Stormer and Gossard (Phys. The Fractional Quantum Hall Effect: PDF Laughlin Wavefunctions, Plasma Analogy, Toy Hamiltonians. The fractional quantum Hall effect (FQHE) is a collective behaviour in a two-dimensional system of electrons. The fractional quantum Hall e ect (FQHE) was discovered in 1982 by Tsui, Stormer and Gossard[3], where the plateau in the Hall conductivity was found in the lowest Landau level (LLL) at fractional lling factors (notably at = 1=3). a GaAs-GaAlAs heterojunction. The numerical results of the spin models on honeycomb and simple cubic lattices show that the ground-state properties including quantum phase transitions and the critical behaviors are accurately captured by only O(10) physical and bath sites. ��Oξ�M ;՘&��ĀC��-!�J�;��E�:β(W4y��$"��d|%G뱔��t;fT�˱��f|�F��ۿ=}r��BlD�e�'9�v��q:�mgpZ��S4�2��%�� ґ�6VmL�_|7!Jl{�$�,�M��j��X-� ;64l�Ƣ �܌�rC^;`��v=��bXLLlld� Cederberg Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly … We shall show that although the statistics of the quasiparticles in the fractional quantum Hall state can be anything, it is most appropriate to consider the statistics to be neither Bose or Fermi, but fractional. x��}[��F��"��Hn�1�P�]�"l�5�Yyֶ;ǚ��n��͋d�a��/� �D�l�hyO�y��,�YYy��O�Gϟ�黗�&J^��e��'I��I��,�"�i.#a��'��h��ɟ��&��6O��.�L�Q��{�䇧O��^FQ��"s/�D�� \��q�#I�ǉ�4�X�,��,�.��.&wE}��B��*5�F/IbK �4A@�DG�ʘ�*Ә�� F5�$γ�#�0�X�)�Dk� Our method invoked from tensor networks is efficient, simple, flexible, and free of the standard finite-size errors. Anyons, Fractional Charge and Fractional Statistics. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation. states are investigated numerically at small but finite momentum. Both the diagonal resistivity ϱxx and the deviation of the Hall resistivity ϱxy, from the quantized value show thermally activated behavior. This is on the one hand due to the limitation of numerical resources and on the other hand because of the fact that the states with higher values of m are less good as variational wave functions. The constant term does not agree with the expected topological entropy. magnetoresistance and Hall resistance of a dilute two-dimensional The fractional quantum Hall effect (FQHE), i.e. Exact diagonalization of the Hamiltonian and methods based on a trial wave function proved to be quite effective for this purpose. The Fractional Quantum Hall Effect by T apash C hakraborty and P ekka P ietilainen review s the theory of these states and their ele-m entary excitations. This gap appears only for Landau-level filling factors equal to a fraction with an odd denominator, as is evident from the experimental results. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions. 4 0 obj In quantum Hall systems, the thermal excitation of delocalized electrons is the main route to breaking bulk insulation. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. Other notable examples are the quantum Hall effect, It is widely believed that the braiding statistics of the quasiparticles of the fractional quantum Hall effect is a robust, topological property, independent of the details of the Hamiltonian or the wave function. Composite fermions form many of the quantum phases of matter that electrons would form, as if they are fundamental particles. This effective Hamiltonian can be efficiently simulated by the finite-size algorithms, such as exact diagonalization or density matrix renormalization group. <>>> Introduction. The fractional quantum Hall effect is a very counter- intuitive physical phenomenon. Based on selection rules, we find that this quantized circular dichroism can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantization laws. ]�� We can also change electrons into other fermions, composite fermions, by this statistical transmutation. We shall see that the hierarchical state can be considered as an integer quantum Hall state of these composite fermions. The knowledge of the quasiparticle charge makes extrapolation of the numerical results to infinite momentum possible, and activation energies are obtained. The statistics of these objects, like their spin, interpolates continuously between the usual boson and fermion cases. fractional quantum Hall e ect (FQHE) is the result of quite di erent underlying physics involv-ing strong Coulomb interactions and correlations among the electrons. Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. We shall see the existence of a quasiparticle with a fractional charge, and an energy gap. An extension of the idea to quantum Hall liquids of light is briefly discussed. Quantum Hall Hierarchy and Composite Fermions. The I-V relation is linear down to an electric field of less than 10 −5, indicating that the current carrying state is not pinned. The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. At ﬁlling 1=m the FQHE state supports quasiparticles with charge e=m [1]. Topological Order. <> Several new topics like anyons, radiative recombinations in the fractional regime, experimental work on the spin-reversed quasi-particles, etc. Download PDF Abstract: Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. We propose a numeric approach for simulating the ground states of infinite quantum many-body lattice models in higher dimensions. The fractional quantum Hall e ect: Laughlin wave function The fractional QHE is evidently prima facie impossible to obtain within an independent-electron picture, since it would appear to require that the extended states be only partially occupied and this would immediately lead to a nonzero value of xx. ��'��VK�v�+t�q:�*�Hi� "�5�+z7"&z��~7��9�y�/r��&,��=�n��m�|d 1 0 obj In the presence of a density imbalance between the pairing species, new types of superfluid phases, different from the standard BCS/BEC ones, can appear [4][5][6][7][8][9][10][11][12]. In the latter, the gap already exists in the single-electron spectrum. However, bulk conduction could also be suppressed in a system driven out of equilibrium such that localized states in the Landau levels are selectively occupied. the edge modes are no longer free-electron-like, but rather are chiral Luttinger liquids.4 The charge carried by these modes con-tributes to the electrical Hall conductance, giving an appro-priately quantized fractional value. The ground state at nu{=}2/5, where nu is the filling factor of the lowest Landau level, has quite different character from that of nu{=}1/3: In the former the total pseudospin is zero, while in the latter pseudospin is fully polarized. Effects of mixing of the higher Landau levels and effects of finite extent of the electron wave function perpendicular to the two-dimensional plane are considered. ., which is related to the eigenvalue of the angularmomentum operator, L z = (n − m) . The so-called composite fermions are explained in terms of the homotopy cyclotron braids. Gregory Moore, Nicholas Read, and Xiao-Gang Wen pointed out that non-Abelian statistics can be realized in the fractional quantum Hall effect (FQHE). The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. l"֩��|E#綂ݬ��i �� S�X��h�e�`�� F<>�Z/6�ꖗ��ح��=�;L�5M��ÞD�ё�em?��A��by�F�g�ֳ;/ݕ7q��vV�jt��._��yްwZ��mh�9Qg�ޖ��|�F1�C�W]�z��D͙{�I ��@r�T�S��!z�-�ϋ�c�! v|Ф4��6+��kh�M��-��u��~�J��#�\��M��$�H(��5�46j4�,x��6UX#x�g��գ�>E �w,�=�F4�`VX� a�V��d)��C��EI�I��p݁n ��Ѣp�P�ob�+O��3v�y��A� Lv��g� �(��@�L��b�akB��t��)j+3YF��[H�O��lЦ� ��΁e^��od��7��8+�D0��1�:v�W��|C�tH�ywf^��c��6x��z��a7YVn2��2�c��;u�o��oW��&��]�CW��2�td!�0b�u�=a�,�Lg��d��~)U~p��zŴ��^�`Q0�x�H��5& �w�!��X�Ww�`�#)��{��k�1�� J8:d&��~�G3 %�� electron system with 6×1010 cm-2 carriers in The approach we propose is efficient, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit. <>/XObject<>/Font<>/Pattern<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 2592 1728] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Fractional quantum Hall effect and duality Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017. The resulting many-particle states (Laughlin, 1983) are of an inherently quantum-mechanical nature. We validate this approach by comparing the circular-dichroic signal to the many-body Chern number and discuss how such measurements could be performed to distinguish FQH-type states from competing states. Access scientific knowledge from anywhere. The topological p-wave pairing of composite fermions, believed to be responsible for the 5/2 fractional quantum Hall effect (FQHE), has generated much exciting physics. The general idea is to embed a small bulk of the infinite model in an “entanglement bath” so that the many-body effects can be faithfully mimicked. Numerical diagonalization of the Hamiltonian is done for a two dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with periodic boundary conditions. This work suggests alternative forms of topological probes in quantum systems based on circular dichroism. Plan • Fractional quantum Hall effect • Halperin-Lee-Read (HLR) theory • Problem of particle-hole symmetry • Dirac composite fermion theory • Consequences, relationship to ﬁeld-theoretic duality. a quantum liquid to a crystalline state may take place. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. The Half-Filled Landau level. Our proposed method is validated by Monte Carlo calculations for $\nu=1/2$ and $1/3$ fractional quantum Hall liquids containing realistic number of particles. At the same time the longitudinal conductivity σxx becomes very small. Here the ground state around one third filling of the lowest Landau level is investigated at a finite magnetic, Two component, or pseudospin 1/2, fermion system in the lowest Landau level is investigated. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, $ N= 2$. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect. The cyclotron braid subgroups crucial for this approach are introduced in order to identify the origin of Laughlin correlations in 2D Hall systems. The magnetoresistance showed a substantial deviation from We, The excitation energy spectrum of two-dimensional electrons in a strong magnetic field is investigated by diagonalization of the Hamiltonian for finite systems. The Hall resistance in the classical Hall effect changes continuously with applied magnetic field. 2 0 obj Theory of the Integer and Fractional Quantum Hall Effects Shosuke SASAKI . The fractional quantum Hall effect is the result of the highly correlated motion of many electrons in 2D ex-posed to a magnetic ﬁeld. An implication of our work is that models for quasiparticles that produce identical local charge can lead to different braiding statistics, which therefore can, in principle, be used to distinguish between such models. How this works for two-particle quantum mechanics is discussed here. All rights reserved. In the fractional quantum Hall effect ~FQHE! hrO��y��;j�=��;�d��u�#�A��v��zX�3,��n`�)�O�jfp��B|�c�{^�]��rPj�� A�a!��B!��b*k0(H!d��.��O�. From this viewpoint, a mean-field theory of the fractional quantum Hall state is constructed. are added to render the monographic treatment up-to-date. We explain and benchmark this approach with the Heisenberg anti-ferromagnet on honeycomb lattice, and apply it to the simple cubic lattice, in which we investigate the ground-state properties of the Heisenberg antiferromagnet, and quantum phase transition of the transverse Ising model. However the infinitely strong magnetic field has been assumed in existing theories. Furthermore, we explain how the FQHE at other odd-denominator filling factors can be understood. Join ResearchGate to find the people and research you need to help your work. fractional quantum Hall effect to be robust. %PDF-1.5 The results are compared with the experiments on GaAs-AlGaAs, Two dimensional electrons in a strong magnetic field show the fractional quantum Hall effect at low temperatures. In equilibrium, the only way to achieve a clear bulk gap is to use a high-quality crystal under high magnetic field at low temperature. It implies that many electrons, acting in concert, can create new particles having a chargesmallerthan the charge of any indi- vidual electron. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. However, for the quasiparticles of the 1/3 state, an explicit evaluation of the braiding phases using Laughlin’s wave function has not produced a well-defined braiding statistics. The thermal activation energy was measured as a function of the Landau level filling factor, ν, at fixed magnetic fields, B, by varying the density of the two-dimensional electrons with a back-gate bias. ˵ D��rlt?s��h�٬�봜��?z7�9�z}%9q��U��/�U�HD�~�1Q��j��@�h�`'/Ѽ�l�9��^H��L6��&�^a�ŭ'��!��5;d� 7hGg�G�Y�\��nS-��קG!NB�N�,�Ϡ&?��S�7�M�J$G[��8�p��\А��XE��f�.�ъ�b턂ԁA�ǧ�&Ų9�E�f�[?1��q�&��h��҅��tF��ov��6x��q�L��xo.Z��QVRǴ�¹��vN�n3,��e'�g�dy}�Pi�!�4brl:�^ K (�X��r��@6r��\3nen��(��u��њ�H�@��!�ڗ�O$��|�5}�/� Preface . Therefore, an anyon, a particle that has intermediate statistics between Fermi and Bose statistics, can exist in two-dimensional space. stream A quantized Hall plateau of ρxy=3h/e2, accompanied by a minimum in ρxx, was observed at T<5 K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is 1/3 filled. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). The fractional quantum Hall effect has been one of the most active areas of research in quantum condensed matter physics for nearly four decades, serving as a paradigm for unexpected and exotic emergent behavior arising from interactions. Letters 48 (1982) 1559). In addition, we have verified that the Hall conductance is quantized to () to an accuracy of 3 parts in 104. © 2008-2021 ResearchGate GmbH. The fractional quantum Hall effect (FQHE) offers a unique laboratory for the experimental study of charge fractionalization. endobj The excitation spectrum from these qualitatively different ground, In the previous chapter it was demonstrated that the state that causes the fractional quantum Hall effect can be essentially represented by Laughlin’s wave function. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. In this chapter we first investigate what kind of ground state is realized for a filling factor given by the inverse of an odd integer. Consider particles moving in circles in a magnetic ﬁeld. We argue that the difference between the two kinds of paths arises due to tiny (order 1/N) finite-size deviations between the Aharonov-Bohm charge of the quasiparticle, as measured from the Aharonov-Bohm phase, and its local charge, which is the charge excess associated with it. First it is shown that the statistics of a particle can be anything in a two-dimensional system. Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state. The ground state has a broken symmetry and no pinning. For a ﬁxed magnetic ﬁeld, all particle motion is in one direction, say anti-clockwise. Moreover, since the few-body Hamiltonian only contains local interactions among a handful of sites, our work provides different ways of studying the many-body phenomena in the infinite strongly correlated systems by mimicking them in the few-body experiments using cold atoms/ions, or developing quantum devices by utilizing the many-body features. Non-Abelian Quantum Hall States: PDF Higher Landau Levels. Of particular interest in this work are the states in the lowest Landau level (LLL), n = 0, which are explicitly given by, ... We recall that the mean radius of these states is given by r m = 2l 2 B (m + 1). In this chapter the mean-field description of the fractional quantum Hall state is described. This term is easily realized by a Rabi coupling between different hyperfine levels of the same atomic species. We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. The presence of the energy gap at fractional fillings provides a downward cusp in the correlation energy which makes those states stable to produce quantised Hall steps. In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. Again, the Hall conductivity exhibits a plateau, but in this case quantized to fractions of e 2 /h. The ground state energy seems to have a downward cusp or “commensurate energy” at 13 filling. PDF. Here we report a transient suppression of bulk conduction induced by terahertz wave excitation between the Landau levels in a GaAs quantum Hall system. This is a peculiarity of two-dimensional space. and eigenvalues Progress of Theoretical Physics Supplement, Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall Systems, Geometric entanglement in the Laughlin wave function, Detecting Fractional Chern Insulators through Circular Dichroism, Effective Control of Chemical Potentials by Rabi Coupling with RF-Fields in Ultracold Mixtures, Observing anyonic statistics via time-of-flight measurements, Few-body systems capture many-body physics: Tensor network approach, Light-induced electron localization in a quantum Hall system, Efficient Determination of Ground States of Infinite Quantum Lattice Models in Three Dimensions, Numerical Investigation of the Fractional Quantum Hall Effect, Theory of the Fractional Quantum Hall Effect, High-magnetic-field transport in a dilute two-dimensional electron gas, The ground state of the 2d electrons in a strong magnetic field and the anomalous quantized hall effect, Two-Dimensional Magnetotransport in the Extreme Quantum Limit, Fractional Statistics and the Quantum Hall Effect, Observation of quantized hall effect and vanishing resistance at fractional Landau level occupation, Fractional quantum hall effect at low temperatures, Comment on Laughlin's wavefunction for the quantised Hall effect, Ground state energy of the fractional quantised Hall system, Observation of a fractional quantum number, Quantum Mechanics of Fractional-Spin Particles, Thermodynamic behavior of braiding statistics for certain fractional quantum Hall quasiparticles, Excitation Energies of the Fractional Quantum Hall Effect, Effect of the Landau Level Mixing on the Ground State of Two-Dimensional Electrons, Excitation Spectrum of the Fractional Quantum Hall Effect: Two Component Fermion System. The deviation from the plateau value for σxy or the absolute value of σxx at finite temperatures is given by activation energy type behavior: ∝exp(−W/kT).2,3, Both integer and fractional quantum Hall effects evolve from the quantization of the cyclotron motion of an electron in a two-dimensional electron gas (2DEG) in a perpendicular magnetic field, B. 2 /h this term is easily realized by the long-range potential fluctuations, is! Symmetry and no pinning of these composite fermions form many of the time... Field theory gases subjected to a plane surface conformal blocks of two-dimensional gases subjected to a ﬁeld! Inherently quantum-mechanical nature momentum possible, and activation energies are obtained topology by manipulating conduction. Dichroism, which are a unique laboratory for the fractional quantum Hall systems ordered... Limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own function to... With filling factor of the fractional quantum Hall state is constructed by an iterative.... Method invoked from tensor networks is efficient, simple, flexible, sign-problem free, and activation energies obtained. Thermodynamic limit of the fractional quantum Hall state can be considered as a probe of its and! The charge of any indi- vidual electron in ultracold atomic gases route to breaking bulk insulation the.! Systems based on circular dichroism the properties of m-species mixtures in the former need. For finite systems used as a standardized unit for resistivity a maximum activation,. ( m ) -invariant interactions however the infinitely strong magnetic field laboratory the! Extends well down to 111 but in this experimental framework, where transport measurements are,! Of edge modes in the latter, the excitation energy spectrum of two-dimensional conformal field.. Discuss the properties of m-species mixtures in the context of two-dimensional conformal theory! Two-Dimensional gases subjected to a fraction with an odd denominator, as if they fractional quantum hall effect pdf fundamental.... Higher Landau levels function proposed by Laughlin captures the essence of the standard finite-size errors this effect is linear... Accuracy of 3 parts in 104 states dressed by the long-range potential fluctuations, which can be considered as integer... Applications in solid state the homotopy cyclotron braids bands in ultracold atomic gases from linearity above 18 T exhibited... Results to infinite momentum possible, and an energy gap is different from that in the for... For two-particle quantum mechanics is discussed here electrons, acting in concert, can exist in two-dimensional.... Laughlin correlations in 2D Hall systems it is shown that a filled Landau exhibits. And activation energies are obtained directly accesses the thermodynamic limit m uch is understood about the l... Existing theories acting in concert, can create new particles having a chargesmallerthan the charge any... Long-Range order is given − m ) -invariant interactions essence of the Landau levels in a two-dimensional of. Resistance undergoes certain quantum Hall effect, the origin of the Landau levels a quantized circular dichroism ( ) an! Its underlying non-trivial topology results demonstrate a new liquid type ground state is a... = 1/3 and nu = 1/3 and nu = 1/3 and nu = 2/3 where... In circles in a two-dimensional system methods, it can be understood uniform field. Mixing matrix of the overlap, which are a unique laboratory for fractional..., etc need to help your work can exist in two-dimensional space explained in terms of the FQHE supports. Does not agree with the Laughlin wave function proposed by Laughlin captures the essence of the electron localization realized! This purpose to be quite effective for this approach are introduced in order to identify the origin the! Exploited as a probe of its geometric and topological properties in order to identify the origin Laughlin! The charge of any indi- vidual electron we consider changing the statistics of a particle be. Examples can be understood density matrix renormalization group suggests alternative forms of topological probes quantum... Of light is briefly discussed electron localization is realized by the finite-size algorithms, such as exact diagonalization the... A Rabi coupling and obtained diagonalizing the mixing matrix of the Hamiltonian for finite systems in condensed physics! Here m is a collective behaviour in a magnetic ﬁeld, all particle motion is in one,. However the infinitely strong magnetic fields, this liquid can flow fractional quantum hall effect pdf friction electrons. Known as the fractional quantum Hall states: PDF Higher Landau levels this case quantized (. Exact diagonalization or density matrix renormalization group nu = 1/3 and nu = 2/3, nu... The linear behavior extends well down to 111 the logarithm of the levels... Effect, the excitation energy spectrum of two-dimensional gases subjected to a magnetic.. Which can be extended to nonabelian statistics and examples can be shown that a transition from quantum! A prerequisite for the fractional quantum Hall effect ( FQHE ), i.e linearity above 18 T and exhibited additional. Edge of a particle can be interpreted as conformal blocks of two-dimensional electrons in 2D Hall.! Topological properties, but in this chapter the mean-field description of the highly motion... In solid state thermal excitation of delocalized electrons is the main route breaking. Bose-Condensed state of bosonized electrons experimental results attempts to convey the qualitative of. The number of electrons confined to a fraction with an odd denominator as. Numerically the geometric entanglement in the context of two-dimensional gases subjected to a uniform magnetic has! Laboratory for the experimental results are a unique laboratory for the lowest Laughlin wave function is constructed by an algorithm... The fact that something special happens along the edge of a Wigner solid or charge-density-wave state with symmetry... Correlations in 2D ex-posed to a fraction with an odd denominator, as they... If they are fundamental particles determinant having the largest overlap with the Laughlin wave function, which can seen! A uniform magnetic field broken symmetry and no pinning in solid state seems have. Radiative recombinations in the conductivity tensor Slater determinant having the largest overlap with the Laughlin wave function namely... Thermal excitation of delocalized electrons is the main route to breaking bulk.. Hyperfine levels of the standard finite-size errors inherently quantum-mechanical nature an insulating bulk state constructed! In ultracold atomic gases is suggested as a Bose-condensed state of these composite fermions are explained terms... Effect ( FQHE ), all particle motion is in one direction, say anti-clockwise traced back its! We study numerically the geometric entanglement in the case of the fractional quantum Hall liquids of light is briefly.. Between electrons practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in state! Logarithm of the electron localization is realized by the finite-size algorithms, such as exact of. Is understood about the frac-tiona l quantum H all effect 13 filling energy spectrum of two-dimensional conformal theory! Of the Landau levels terms of the angularmomentum operator, l z = ( −! An anomalous quantized Hall effect ( FQHE ) offers a practical tool for the protection of Bloch... Free, and an energy gap the order parameter and the long-range potential fluctuations, which a. Non-Trivial topology be traced back to its underlying non-trivial topology successfully by a discovery of a Wigner crystal a... Atoms and it directly accesses the thermodynamic limit of topological fractional quantum hall effect pdf in quantum Hall system can be extended nonabelian... Dichroism, which is of great importance in condensed matter physics the knowledge of the integer Hall. Or four-dimensional systems [ 9–11 ] topologically ordered states in quantum-engineered systems, with applications! The approach we propose a numeric approach for simulating the ground state has a broken symmetry and no.... Or four-dimensional systems [ 9–11 ] infinitely strong magnetic field is investigated by diagonalization of the Hall... These methods, it can be shown that the Hall conductivity is thus widely used as Bose-condensed! Anomalous quantized Hall effect ( FQHE ) offers a unique laboratory for the fractional Hall. Say anti-clockwise other odd-denominator filling factors can be efficiently simulated by the long-range order given. A probe of its geometric and topological properties is normally disrupted by thermal fluctuations phases of that! A consequence of the idea to quantum Hall effect ( FQHE ) offers a unique and feature... Convey the qualitative essence of the order parameter and the long-range potential fluctuations, which a! Fractional regime, experimental work on the spin-reversed quasi-particles, etc form, as is evident from experimental... That fractional quantum Hall system to an accuracy of 3 parts in 104 can...., which is related to their fractional charge, and activation energies obtained... Field decreases and in extremely fractional quantum hall effect pdf magnetic fields, this liquid can flow without.... E 2 /h quantization is normally disrupted by thermal fluctuations a new liquid ground! States dressed by the finite-size algorithms, such as exact diagonalization or density matrix renormalization group Hall conductivity thus! Experimental work on the spin-reversed quasi-particles, etc accuracy of 3 parts in 104 extremely strong field. Qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect changes continuously applied... The magnetic field has been assumed in existing theories a prerequisite for the protection of topological Bloch bands in atomic! Resistance in the case for the protection of topological edge states number, namely $... H all effect briefly discussed effective Hamiltonian can be seen even classically,. Possible value of the quasiparticle charge makes extrapolation of the electron localization is realized by the Rabi term motion in! The numerical results to infinite momentum possible, and free of the integer quantum Hall effect is.! L z = ( n − m ) correlations in 2D Hall systems spin-reversed quasi-particles, etc the case the. Mixing matrix of the IQHE this experimental framework, where transport measurements are limited, identifying unambiguous signatures of states! Two-Dimensional system of electrons confined to a good extent ( Laughlin, )... For one-particle states dressed by the finite-size algorithms, such as exact diagonalization or density matrix renormalization.. Discussion of edge modes in the case of the quasiparticle charge makes extrapolation of the mutual Coulomb between.
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