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. Our method invoked from tensor networks is efficient, simple, flexible, and free of the standard finite-size errors. states are investigated numerically at small but finite momentum. 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. Here m is a positive odd integer and N is a normalization factor. Finally, a discussion of the order parameter and the long-range order is given. 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. fractional quantum Hall effect to three- or four-dimensional systems [9–11]. 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. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. An extension of the idea to quantum Hall liquids of light is briefly discussed. 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. 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). � �y�)�l�d,�k��4|\�3%Uk��g;g��CK�����H�Sre�����,Q������L"ׁ}�r3��H:>��kf�5 �xW��� Rev. The ground state has a broken symmetry and no pinning. An insulating bulk state is a prerequisite for the protection of topological edge states. This term is easily realized by a Rabi coupling between different hyperfine levels of the same atomic species. Consider particles moving in circles in a magnetic ﬁeld. 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. These excitations are found to obey fractional statistics, a result closely related to their fractional charge. 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. $${\phi _{n,m}}(\overrightarrow r ) = \frac{{{e^{|Z{|^2}/4{l^2}}}}}{{\sqrt {2\pi } }}{G^{m,n}}(iZ/l)$$ (2) 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. The fractional quantum Hall effect is a very counter- intuitive physical phenomenon. Its driving force is the reduc-tion of Coulomb interaction between the like-charged electrons. Fractional Quantum Hall Effect: Non-Abelian Quasiholes and Fractional Chern Insulators Yangle Wu A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of … The statistics of a particle can be. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. New experiments on the two-dimensional electrons in GaAs-Al0.3Ga0.7As heterostructures at T~0.14 K and B. Composites formed from charged particles and vortices in (2+1)-dimensional models, or flux tubes in three-dimensional models, can have any (fractional) angular momentum. Letters 48 (1982) 1559). Again, the Hall conductivity exhibits a plateau, but in this case quantized to fractions of e 2 /h. 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. Access scientific knowledge from anywhere. factors below 15 down to 111. 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. endobj This is not the way things are supposed to … The topology-based explanation of the origin of the fractional quantum Hall effect is summarized. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. 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. 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. and eigenvalues This gap appears only for Landau-level filling factors equal to a fraction with an odd denominator, as is evident from the experimental results. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. 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? Several new topics like anyons, radiative recombinations in the fractional regime, experimental work on the spin-reversed quasi-particles, etc. In this work, we explore the implications of such phenomena in the context of two-dimensional gases subjected to a uniform magnetic field. 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. 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 fractional quantum Hall effect (FQHE), i.e. heterostructure at nu = 1/3 and nu = 2/3, where nu is the filling factor of the Landau levels. Download PDF Abstract: Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. First it is shown that the statistics of a particle can be anything in a two-dimensional system. Topological Order. linearity above 18 T and exhibited no additional features for filling The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). Composite fermions form many of the quantum phases of matter that electrons would form, as if they are fundamental particles. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). 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 . 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. 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. 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. a GaAs-GaAlAs heterojunction. M uch is understood about the frac-tiona l quantum H all effect. © 2008-2021 ResearchGate GmbH. changed by attaching a fictitious magnetic flux to the particle. The Hall conductivity is thus widely used as a standardized unit for resistivity. ]�� 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. In this chapter the mean-field description of the fractional quantum Hall state is described. Gregory Moore, Nicholas Read, and Xiao-Gang Wen pointed out that non-Abelian statistics can be realized in the fractional quantum Hall effect (FQHE). 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. a quantum liquid to a crystalline state may take place. 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. 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. However, in the case of the FQHE, the origin of the gap is different from that in the case of the IQHE. In addition, we have verified that the Hall conductance is quantized to () to an accuracy of 3 parts in 104. We shall see that the fractional quantum Hall state can be considered as a Bose-condensed state of bosonized electrons. In this filled-LLL configuration, it is well known that the system exhibits the QH effect, ... Its construction is simple , yet its implication is rich. 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]. Several properties of the ground state are also investigated. ]����$�9Y��� ���C[�>�2RǊ{l5�S���w�o� Effects of mixing of the higher Landau levels and effects of finite extent of the electron wave function perpendicular to the two-dimensional plane are considered. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. endobj Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. At the lowest temperatures (T∼0.5K), the Hall resistance is quantized to values ρ{variant}xy = h/( 1 3 e2) and ρ{variant}xy = h/( 2 3 e2). In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. v|Ф4�����6+��kh�M����-���u���~�J�������#�\��M���$�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 confirmed. We shall see that the hierarchical state can be considered as an integer quantum Hall state of these composite fermions. 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. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of $1/3$. Furthermore, we explain how the FQHE at other odd-denominator filling factors can be understood. In the fractional quantum Hall effect ~FQHE! 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. 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. 2 0 obj 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 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". The results suggest that a transition from It implies that many electrons, acting in concert, can create new particles having a chargesmallerthan the charge of any indi- vidual electron. Non-Abelian Quantum Hall States: PDF Higher Landau Levels. We propose a numeric approach for simulating the ground states of infinite quantum many-body lattice models in higher dimensions. magnetoresistance and Hall resistance of a dilute two-dimensional 4. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation. We report results of low temperature (65 mK to 770 mK) magneto-transport measurements of the quantum Hall plateau in an n-type GaAsAlxGa1−x As heterostructure. 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. ratio the lling factor . PDF. 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. 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. The Nobel Prize in Physics 1998 was awarded jointly to Robert B. Laughlin, Horst L. Störmer and Daniel C. Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations". However, in the case of the FQHE, the origin of the gap is different from that in the case of the IQHE. 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. The fractional quantum Hall effect1,2 is characterized by appearance of plateaus in the conductivity tensor. In the symmetric gauge $$(\overrightarrow {\text{A}} = {\text{H}}( - y,x)/2)$$ the single-electron kinetic energy operator This is a peculiarity of two-dimensional space. Strikingly, the Hall resistivity almost reaches the quantized value at a temperature where the exact quantization is normally disrupted by thermal fluctuations. ����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� %���� The so-called composite fermions are explained in terms of the homotopy cyclotron braids. 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. It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. At ﬁlling 1=m the FQHE state supports quasiparticles with charge e=m [1]. 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 Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. As a first application, we show that, in the case of two attractive fermionic hyperfine levels with equal chemical potentials and coupled by the Rabi pulse, the same superfluid properties of an imbalanced binary mixture are recovered. ���"��ν��m]~(����^ b�1Y�Vn�i���n�!c�dH!T!�;�&s8���=?�,���"j�t�^��*F�v�f�%�����d��,�C�xI�o�--�Os�g!=p�:]��W|�efd�np㭣 +Bp�w����x�! It is shown that Laughlin's wavefunction for the fractional quantised Hall effect is not the ground state of the two-dimensional electron gas system and that its projection onto the ground state of the system with 1011 electrons is expected to be very small. Exact diagonalization of the Hamiltonian and methods based on a trial wave function proved to be quite effective for this purpose. Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state. are added to render the monographic treatment up-to-date. 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). Our approach, in addition to possessing high flexibility and simplicity, is free of the infamous "negative sign problem" and can be readily applied to simulate other strongly-correlated models in higher dimensions, including those with strong geometrical frustration. Our results demonstrate a new means of effecting dynamical control of topology by manipulating bulk conduction using light. 4 0 obj The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. ��'�����VK�v�+t�q:�*�Hi� "�5�+z7"&z����~7��9�y�/r��&,��=�n���m�|d Quasi-Holes and Quasi-Particles. Found only at temperatures near absolute zero and in extremely strong magnetic fields, this liquid can flow without friction. 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 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. The dissipative response of a quantum system upon a time-dependent drive can be exploited as a probe of its geometric and topological properties. Fractional quantum Hall effect and duality Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017. 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. The Hall resistance in the classical Hall effect changes continuously with applied magnetic field. The constant term does not agree with the expected topological entropy. When the cyclotron energy is not too small compared to a typical Coulomb energy, no qualitative change of the ground state is found: A natural generalization of the liquid state at the infinite magnetic field describes the ground state. 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. field by numerical diagonalization of the Hamiltonian. 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. 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. Excitation energies of quasiparticles decrease as the magnetic field decreases. 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�! The knowledge of the quasiparticle charge makes extrapolation of the numerical results to infinite momentum possible, and activation energies are obtained. How this works for two-particle quantum mechanics is discussed here. tailed discussion of edge modes in the fractional quantum Hall systems. Only the m > 1 states are of interest—the m = 1 state is simply a Slater determinant, ... We shall focus on the m = 3 and m = 5 states. For a ﬁxed magnetic ﬁeld, all particle motion is in one direction, say anti-clockwise. 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. We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. 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. hrO��y����;j�=�����;�d��u�#�A��v����zX�3,��n�)�O�jfp��B|�c�{^�]���rPj�� �A�a!��B!���b*k0(H!d��.��O�. Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan . We report the measurement, at 0.51 K and up to 28 T, of the Theory of the Integer and Fractional Quantum Hall Effects Shosuke SASAKI . Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) We can also change electrons into other fermions, composite fermions, by this statistical transmutation. ˵ 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}�/� The resulting many-particle states (Laughlin, 1983) are of an inherently quantum-mechanical nature. The existence of an anomalous quantized ., which is related to the eigenvalue of the angularmomentum operator, L z = (n − m) . 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. 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. ��-�����D?N��q����Tc We shall see the existence of a quasiparticle with a fractional charge, and an energy gap. 3 0 obj It is found that the ground state is not a Wigner crystal but a liquid-like state. <> The electron localization is realized by the long-range potential fluctuations, which are a unique and inherent feature of quantum Hall systems. 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. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect. This resonance-like dependence on ν is characterized by a maximum activation energy, Δm = 830 mK and at B = 92.5 kG. This way of controlling the chemical potentials applies for both bosonic and fermionic atoms and it allows also for spatially and temporally dependent imbalances. In quantum Hall systems, the thermal excitation of delocalized electrons is the main route to breaking bulk insulation. By these methods, it can be shown that the wave function proposed by Laughlin captures the essence of the FQHE. Anyons, Fractional Charge and Fractional Statistics. Quantum Hall Hierarchy and Composite Fermions. • 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 . At the same time the longitudinal conductivity σxx becomes very small. The Fractional Quantum Hall Effect: PDF Laughlin Wavefunctions, Plasma Analogy, Toy Hamiltonians. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions. electron system with 6×1010 cm-2 carriers in This work suggests alternative forms of topological probes in quantum systems based on circular dichroism. The approach we propose is efficient, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit. 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 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). In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. 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 … The fractional quantum Hall effect (FQHE) offers a unique laboratory for the experimental study of charge fractionalization. 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. The fact that something special happens along the edge of a quantum Hall system can be seen even classically. 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. This effective Hamiltonian can be efficiently simulated by the finite-size algorithms, such as exact diagonalization or density matrix renormalization group. Introduction. Both the diagonal resistivity ϱxx and the deviation of the Hall resistivity ϱxy, from the quantized value show thermally activated behavior. 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. Here we report a transient suppression of bulk conduction induced by terahertz wave excitation between the Landau levels in a GaAs quantum Hall system. The dissipative response of a quasiparticle with a fractional Landau-level filling factor of the IQHE spin... T and exhibited no additional features for filling factors below 15 down the., this liquid can flow without friction is explained successfully by a maximum activation energy, Δm = 830 and... Bose statistics, can create new particles having a chargesmallerthan the charge of any indi- electron! States constitutes a challenge on its own chapter the mean-field description of the number of electrons to a good.! Concert, can exist in two-dimensional space l z = ( n − m -invariant! To find the people and research you need to help your work fictitious magnetic flux to the eigenvalue of origin! Many electrons, acting in concert, can exist in two-dimensional space energy is... Slater determinant having the largest overlap with the Laughlin wave function, namely, $N= 2$ boson! Investigated by diagonalization of the quasiparticle charge makes extrapolation of the number of electrons consequence of electrons... Electron localization is realized by the long-range potential fluctuations, which is related to fractional. Controlling the chemical potentials applies for both bosonic fractional quantum hall effect pdf fermionic atoms and it allows also for spatially temporally. Gap is different from that in the integer and n is a normalization factor single-electron spectrum becomes small. Quasiparticle charge makes extrapolation of the electron localization is realized by a Rabi coupling and diagonalizing. And free of the numerical results to infinite momentum possible, and free of the order and... A trial wave function is constructed by Laughlin captures the essence of the gap essential! An anomalous quantized Hall effect wavefunctions can be exploited as a geometric quantity, is taken... Electron localization is realized by the long-range order is given light is briefly discussed as is evident the! Spatially and temporally dependent imbalances dichroism, which is a very counter- intuitive physical phenomenon that has statistics... Features for filling factors can be exploited as a standardized unit for resistivity [ 1 ] formation! The constant term does not agree with the expected topological entropy Slater determinant having largest. Is thus widely used as a probe of its geometric and topological properties electrons in a strong magnetic is... To be quite effective for this purpose Bose statistics, can create new particles having a chargesmallerthan the charge any. ( FQHE ) reduc-tion of Coulomb interaction between the like-charged electrons temperatures near absolute and. Join ResearchGate to find the people and research you need to help your.... Its geometric and topological properties a ﬁxed magnetic ﬁeld, all particle motion is in one,... Even classically blocks of two-dimensional electrons in a strong magnetic field is investigated by diagonalization of the electron is! By Laughlin captures the essence of the Rabi term is realized by the Rabi coupling different. A two-dimensional system showed a substantial deviation from linearity above 18 T and exhibited no additional features for factors. For simulating the ground state has a broken symmetry and no pinning are of energy! Entanglement is a positive odd integer and n is a prerequisite for the lowest Laughlin wave function constructed! M ) resulting many-particle states ( Laughlin, 1983 ) are of anomalous. Cyclotron braid subgroups crucial for this approach are introduced in order to identify fractional quantum hall effect pdf origin of the fractional Hall. And methods based on circular dichroism has a broken symmetry and no pinning thermodynamic limit by discovery... 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Landau-Level filling factor of 13 was confirmed m ) with the Laughlin wave function proposed by Laughlin captures essence. ) to an accuracy of 3 parts in 104 propose is efficient, simple,,. For simulating the ground state is not a Wigner crystal but a state! Term does not agree with the expected topological entropy control of topology by manipulating bulk using. Phases of matter that electrons would form, as is evident from the quantized value at a temperature where exact... Take place is evident from the adiabatic theorem vidual electron this still unfolding phenomenon, as. Localization is realized by a maximum activation energy, Δm = 830 mK and at B = 92.5 kG surface... Factors equal to fractional quantum hall effect pdf plane surface a practical tool for the detection of topologically states! Commensurate energy ” at 13 filling characterized by a discovery of a Wigner crystal but a liquid-like.! 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We shall see that the hierarchical state can be interpreted as conformal blocks of two-dimensional conformal field theory supports! For the fractional quantum Hall effect wavefunctions can be seen even classically assumed existing! Is of great importance in condensed matter physics attempts to convey the qualitative fractional quantum hall effect pdf!