Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session N65: Fractional Quantum Hall Effect: Theory and NumericsRecordings Available
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Sponsoring Units: DCMP Chair: Hart Goldman, MIT Room: Hyatt Regency Hotel -Grant Park C |
Wednesday, March 16, 2022 11:30AM - 11:42AM |
N65.00001: Lowest Landau level theory of the bosonic Jain states Hart Goldman, Senthil Todadri Quantum Hall systems offer the most familiar setting where strong inter-particle interactions combine with the topology of single particle states to yield novel phenomena. Despite our mature understanding of these systems, an open challenge has been to to develop a microscopic theory capturing both their universal and non-universal properties, when the Hamiltonian is restricted to the non-commutative space of the lowest Landau level. Here we develop such a theory for the Jain sequence of bosonic fractional quantum Hall states at fillings \nu = p/(p+1). Building on a lowest Landau level description of a parent composite fermi liquid at \nu = 1, we describe how to dope the system to reach the Jain states. Upon doping, the composite fermions fill non-commutative generalizations of Landau levels, and the Jain states correspond to integer composite fermion filling. Using this approach, we obtain an approximate expression for the bosonic Jain sequence gaps with no reference to any long-wavelength approximation. Furthermore, we show that the universal properties, such as Hall conductivity, are encoded in an effective non-commutative Chern-Simons theory, which is obtained on integrating out the composite fermions. This theory has the same topological content as the familiar Abelian Chern-Simons theory on commutative space. |
Wednesday, March 16, 2022 11:42AM - 11:54AM |
N65.00002: Dirac Composite Fermion Theory of General Jain's Sequences Dung X Nguyen, Dam T Son We reconsider the composite fermion theory of general Jain's sequences with filling factor N/(4N+1). We show that the previous proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the coefficient of the static structure factor. To resolve this apparent contradiction, we add to the effective theory a gapped chiral mode that already exists in the Fermi liquid state at 1/4. We interpret the additional mode as an internal degree of freedom of the composite fermion In addition to providing a suitable static structure factor, our model also gives the expected Wen-Zee shift and a Hall conductivity that manifests Galilean invariance. The extra mode can be detected by circular polarized Raman scattering experiments. |
Wednesday, March 16, 2022 11:54AM - 12:06PM |
N65.00003: BCS pairing of composite fermions in wide quantum wells Anirban Sharma, Songyang Pu, Jainendra K Jain There is evidence for fractional quantum Hall effect at $\nu = 1/4$ in wide GaAs quantum wells [1]. This state has been predicted, in variational studies, to be topologically distinct from the Pfaffian state [2]. We investigate the problem by constructing BCS wave functions of composite fermions for different pairing channels. We minimize the Coulomb interaction energy by varying two variational parameters of the wave function, namely the gap parameter and a momentum cutoff analogous to the Debye frequency in BCS formalism. We search for a pairing instability as a function of the well width and electron density. |
Wednesday, March 16, 2022 12:06PM - 12:18PM |
N65.00004: Anderson localization in fractional quantum Hall effect Songyang Pu, G. J. Sreejith, Jainendra K Jain The interplay between interaction and disorder-induced localization is of fundamental interest. Our work addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor ν = n/(2n + 1) has a striking quantitative correspondence to the localization of a single electron in the (n + 1)th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean-field approximation, these results can be extended to situations where a finite density of quasiparticles is present. |
Wednesday, March 16, 2022 12:18PM - 12:30PM |
N65.00005: Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study Prashant Kumar, Frederick D M Haldane We use the dynamical structure factors of the quantum Hall states at ν=1/3 and ν=1/2 to study their excitation spectrum. Using the density matrix renormalization group in combination with the time-dependent variational principle on an infinite cylinder geometry, we extract the low energy properties. At ν=1/3, a sharp magnetoroton mode and the two-roton continuum agree with the fractionally charged quasi-particles picture. At ν=1/2, we find low energy modes with linear dispersion and the static structure factor s(q) ~ (q lB)^3 in the limit q lB → 0. The properties of these modes can be explained by the quasi-1D composite-fermion theory. |
Wednesday, March 16, 2022 12:30PM - 12:42PM |
N65.00006: Possible stripe phase at ν=7/3 in the presence of mass anisotropy Ravindra N Bhatt, Prashant Kumar We study the phase diagram of ν=7/3 in the n=1 Landau level in the presence of a (two-fold) mass anisotropy. Using the density matrix renormalization group method on an infinite cylinder geometry with varying circumference, we find a continuous transition from the Laughlin fractional quantum Hall state to a stripe phase with a period of ~ 5.5lB. The transition is driven by the condensation of the magnetoroton which becomes gapless at the critical point. The transition, in principle, could survive in the 2D limit and be observed in experiments. |
Wednesday, March 16, 2022 12:42PM - 12:54PM |
N65.00007: Defining the Incompressibility of 2/5 Fractional Quantum Hall State through Gapless Gaffnian State Sahana Das, Sudipto Das, Sutirtha Mukherjee, Sudhansu S Mandal One of the widely studied fractional quantum Hall states at filling factor 2/5 was portrayed as the so-called Gaffnian state [1], which produces a very high overlap with the exact Coulomb state although it was modeled from non-unitary conformal field theory, thus failing to produce a gaped quantum Hall state. Due to this fact, it was suggested to be a quantum critical point. By recasting the Gaffnian wave function as the inter-flavor pairing of the composite fermions (CFs), we introduce a modified Gaffnian wave function by changing the flux correlations of only two pairs of CFs. A suitable linear combination of these two wave functions has excellent overlap with the exact Coulomb ground state. Agreement of the entanglement spectra corresponding to this mixed wave function and the exact ground-state wave function is found up to much higher energies in comparison to the lone Gaffnian wave function. In contrary to the Gaffnian wave function, this mixed wave function’s overlap with the exact ground state of a hybrid three-body and two-body model Hamiltonian gradually increases with the increase of latter’s weight and eventually becomes almost unity. |
Wednesday, March 16, 2022 12:54PM - 1:06PM |
N65.00008: Entanglement Action for the Real-Space Entanglement Spectra of Chiral Abelian Quantum Hall Wave Functions Greg J Henderson, Steven H Simon, G. J. Sreejith We argue and numerically substantiate that the real-space entanglement spectrum (RSES) of chiral abelian quantum Hall states is given by the spectrum of a local boundary perturbation of a (1+1)d conformal field theory, which describes an effective edge dynamics along the real-space cut. The cut-and-glue approach suggests that the low-lying RSES is equivalent to the low-lying modes of some effective edge action. The general structure of this action is deduced by mapping to a boundary critical problem, generalizing work of Dubail, Read, and Rezayi [PRB 85, 11531 (2012)]. Using trial wave functions we numerically test our model of the RSES for the ν = 2/3 bosonic composite fermion state. |
Wednesday, March 16, 2022 1:06PM - 1:18PM |
N65.00009: Fractional charge pumping of anyons and the adiabatic heuristic principle Koji Kudo, Yoshihito Kuno, Yasuhiro Hatsugai By using the Laughlin's argument on a torus with two pin-holes, the fractional charge pumping of anyons is numerically demonstrated. We have confirmed that the general feature of the energy spectra remains unchanged during the flux-attachment transformation of the adiabatic heuristic principle, even though the topological degeneracy is wildly changed. The total jump of the center-of-mass induced by the Laughlin's flux insertion works well as an invariant during this process. This result is consistent with the bulk-edge correspondence of the fractional quantum Hall effect of anyons [1]. |
Wednesday, March 16, 2022 1:18PM - 1:30PM |
N65.00010: Solvable Lattice Hamiltonians with Fracitonal Hall Conductivity Jing-Yuan Chen, Zhaoyu Han We construct a class of lattice Hamiltonians -- both bosonic and fermionic ones -- that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem. More broadly, our work may shed light on the general study of the symmetry enriched topological phases which have gapless edges protected by symmetry. |
Wednesday, March 16, 2022 1:30PM - 1:42PM |
N65.00011: Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications Yuzhu Wang Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. Here, we show a set of analytical results for the energy gap of the graviton modes with two-body and three-body Hamiltonians in both the long-wavelength and the thermodynamic limit. These allow us to construct model Hamiltonians for the graviton modes in different FQH phases, and to elucidate a hierarchical structure of conformal Hilbert spaces (null spaces of model Hamiltonians) with respect to the graviton modes and their corresponding ground states. Numerical results of the Laughlin ν= 1/5 and the Gaffnian ν= 2/5 phases confirm that for gapped phases, low-lying neutral excitations can undergo a "phase transition" even when the ground state is invariant. We discuss the compressibility of the Gaffnian phase, the possibility of multiple graviton modes, and the transition from the graviton modes to the "hollow-core" modes, as well as their experimental consequences. |
Wednesday, March 16, 2022 1:42PM - 1:54PM |
N65.00012: Statistical interactions and boson-anyon duality in fractional quantum Hall fluids Bo Yang We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For interacting electrons, the statistical transmutation from anyons to bosons allows us to explicitly derive the microscopic statistical interaction between the anyons, in the form of the effective two-body and few-body interactions. This also leads to a number of unexpected topological phases of the single component bosonic fractional quantum Hall effect that may be experimentally accessible. Numerical analysis of the energy spectrum and ground state entanglement properties are carried out for simple examples. We also discuss an exact unitary transformation between electrons and composite fermions and a fractal structure of the possible FQH states, as well as the experimental implications of anyon statistics in the presence of disorder. (Bo Yang, Phys. Rev. Lett. 127, 126406 (2021)) |
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