Bulletin of the American Physical Society
APS March Meeting 2021
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session A46: Fractional Quantum Hall Effect ILive

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Sponsoring Units: DCMP Chair: Jie Wang, Flatiron Institute 
Monday, March 15, 2021 8:00AM  8:12AM 
A46.00001: Thermal equilibration on the edges of topological liquids Kwok Wai Ma, Dmitri Feldman Thermal conductance has emerged as a powerful probe of topological order in the quantum Hall effect and beyond. The interpretation of experiments depends on the ratio of the sample size and the equilibration length, on which energy exchange among contrapropagating chiral modes becomes significant. We show that at low temperatures the equilibration length diverges as 1/T^2 for almost all Abelian and nonAbelian topological orders. A faster 1/T^4 divergence is present on the edges of the nonAbelian PHPfaffian and negativeflux ReadRezayi liquids. We address experimental consequences of the 1/T^2 and 1/T^4 laws in a sample, shorter than the equilibration length. 
Monday, March 15, 2021 8:12AM  8:24AM Live 
A46.00002: Vanishing thermal equilibration for holeconjugate fractional quantum Hall states in graphene SAURABH SRIVASTAV, Ravi Kumar, Christian Spånslätt, Kenji Watanabe, Takashi Taniguchi, Alexander Mirlin, Yuval Gefen, Anindya Das Transport through edgechannels is responsible for conduction in quantum Hall (QH) phases. Topology dictates the quantization of both charge and thermal transport coefficients. These turn out to approach robust quantized values when incoherent equilibration processes become dominant. Here, we report on measurements of both electrical and thermal conductances of integer and fractional quantum Hall (FQH) phases, realized in hBN encapsulated graphite gated bilayer graphene devices. Remarkably, for the complex edge at filling factors ν = 5/3 and ν = 8/3, which correspond to the paradigmatic holeconjugate FQH phase ν = 2/3 of the partially filled Landau level, we find vanishing thermal equilibration. This is striking, given that, at the same time, our results for the electrical conductance indicate efficient charge equilibration. These results are in accord with our theoretical analysis, pointing to a divergent thermal equilibration length in the limit of strong electrostatic interaction. Our results elucidate the subtle nature of the crossover from mesoscopic to robust topologydominated transport in electronic twodimensional topological phases. 
Monday, March 15, 2021 8:24AM  8:36AM Live 
A46.00003: Probing spin structure of mangetoroton with Raman scattering Dung Nguyen, Dam Thanh Son We construct a new model for Raman scattering on a fractional Quantum Hall (FQH) state. We use the Luttinger model of GaAs to construct an effective coupling of the lowest Landau level (LLL) electrons with photons. Unlike the previous argument that the light scattering spectra of Raman scattering are associated with the dynamical structure factor, our results show that the scattering signal is mainly due to the kinetic part of the stressenergy tensor correlation functions. We also propose an experimental setup to test the hypothesis on the spin structure of the magnetoroton excitations. 
Monday, March 15, 2021 8:36AM  8:48AM Live 
A46.00004: The boundary density profile of a Coulomb droplet. Freezing at the edge. Gabriel Jose Goulart Cardoso, JeanMarie Stéphan, Alexandre G Abanov Motivated by Laughlin’s plasma analogy, we revisit the problem of computing the boundary density profile of a droplet of twodimensional onecomponent plasma (2D OCP) with logarithmic interaction between particles in a confining harmonic potential. At a sufficiently low temperature, but still in the liquid phase, the density exhibits oscillations as a function of the distance to the boundary of the droplet. We obtain the density profile numerically using MonteCarlo simulations of the 2D OCP. We argue that the decay and period of those oscillations can be explained within a picture of the Wigner crystallization near the boundary, where the crystal is gradually melted with the increasing distance to the boundary. The 2D OCP appears in connection to many different problems: the electron density of Laughlin’s wave function, certain random matrix ensembles, and chiral vortex fluids. Reference: arXiv:2009.02359 
Monday, March 15, 2021 8:48AM  9:00AM Live 
A46.00005: Model wavefunctions for interfaces between lattice Laughlin states Blazej Jaworowski, Anne E. B. Nielsen The interfaces between topological orders are predicted to display nontrivial phenomena, e.g., the anyonic Andreev reflection. However, for chiral topological orders (such as quantum Hall states), they are hard to study microscopically, because of the required system size and the lack of exactly solvable models. 
Monday, March 15, 2021 9:00AM  9:12AM Live 
A46.00006: Fractional Quantum Hall Effect in Arbitrary Potentials Yayun Hu, Yang Ge, Jianxiao Zhang, Jainendra Jain A KohnSham density functional theory (DFT) of composite fermions (CFs) takes into account the flux attached to CFs in a selfconsistent fashion [1,2]. We develop numerical methods that allow the treatment of fractional quantum Hall effect (FQHE) systems in arbitrary potentials without rotational symmetry. This will enable realistic modeling of the experimental setups of FQHE in mesoscopic devices by taking into account the effect of irregular geometries, disorder, anisotropy, etc. As an application, we study the evolution of the ground state density in FQHE with respect to the strength of the exchangecorrelation potential of CFs and find the appearance of charge density waves as the exchangecorrelation potential increases in magnitude. 
Monday, March 15, 2021 9:12AM  9:24AM Live 
A46.00007: Largescale simulations of PHPfaffian trial wave functions Mykhailo Yutushui, David F. Mross The $\nu=5/2$ fractional quantum Hall plateau is generally attributed to pairing of composite fermions. Numerics support the antiPfaffian topological order at this filling, but recent experiments instead indicate a PHPfaffian phase. A trial wave function for the latter has been proposed, but the need for projection into the lowest Landau level has severely constrained the numerically accessible system sizes. In my talk, I will first introduce a family of pairedcompositefermion trial states for \textit{any} odd Cooperpair angular momentum, which can be efficiently projected into the lowest Landau level for large system sizes. I will then present numerical evidence that projecting the PHPfaffian trial state results in a gapless composite Fermi liquid. 
Monday, March 15, 2021 9:24AM  9:36AM Live 
A46.00008: Fractional quantum Hall states: Frustrationfree parent Hamiltonians and infinitebonddimension matrixproductstates Matheus Schossler, Sumanta Bandyopadhyay, Alexander Seidel The study of frustrationfree (FF) Hamiltonians and its relation to finite bond dimension matrixproductstates (MPS) has a long tradition. However, fractional quantum hall states (FQHS) do not quite follow this theme, since the known MPS representation of their ground states have infinitebonddimension. We present the beginnings of a framework for FF Hamiltonians with infinite bond dimensions MPS ground states. In doing so, we abandon the long established approach of deriving and analyzing FQHS parent Hamiltonians through analytic functions and clustering properties, replacing the latter by infinitebonddimension MPS and inductive schemes in particle number. We show how the parent Hamiltonians for Laughlin and MooreRead states, which feature zero energy bosonic and/or Majorana excitations, are directly connected to the MPS representation. A possible extension to parent Hamiltonians for unprojected Jain states and their multicomponent bosonic conformal field theory/MPS descriptions are also discussed. 
Monday, March 15, 2021 9:36AM  9:48AM Live 
A46.00009: Nondiagonal anisotropic quantum Hall states Pok Man Tam, Charles L Kane We introduce a family of Abelian quantum Hall states termed the nondiagonal states, arising at filling ν = p/2q for bosonic systems and ν = p/(p + 2q) for fermionic systems, with p and q being two coprime integers. Nondiagonal states are constructed in a coupled wire model, which shows an intimate relation to the nondiagonal conformal field theory and features quasiparticles with constrained motion. From the quasiparticle braiding statistics, we establish the nondiagonal state as a symmetryenriched topological order that mixes a Laughlin state with a Z_{p} toric code. Two symmetries are relevant: the U(1) charge symmetry and the Z translation symmetry of the wire model. In particular, translation symmetry distinguishes nondiagonal states from Laughlin states, in a way similar to how it distinguishes weak topological insulators from trivial band insulators. Moreover, translation symmetry in nondiagonal states is associated to the e ↔ m anyonic symmetry in Z_{p }toric code, implying the role of dislocations as twofold twistdefects. Thus, our microscopic model also provides a route of realizing an isotropic nonAbelian states through the melting of wire model. 
Monday, March 15, 2021 9:48AM  10:00AM Live 
A46.00010: Generalized Streda formula in the adiabatic heuristic principle Koji Kudo, Yasuhiro Hatsugai The adiabatic heuristic principle for the quantum Hall (QH) states are numerically demonstrated under the algebraic constraints of the Braid group on a torus. The manybody gap is smooth and finite when the Hamiltonian is adiabatically deformed by the flux attachement from the fractional QH state to the integer one. The manybody Chern number of the ground state multiplet works well as an adiabatic invariant for the gap while their topological degeneracy changes wildly. Assuming the invariance of the manybody Chern number, we have analytically proved a generalized Streda formula, which explains the wild behavior of the topological degeneracy in terms of the Chern number. [1] 
Monday, March 15, 2021 10:00AM  10:12AM Live 
A46.00011: Rotons in Anyon Superfluids Umang Mehta, YiHsien Du, Dam Thanh Son We compute the spectrum of excitations for anyon superfluids near statistical angle \pi beyond the massless NambuGoldstone boson of the superfluid. Modeling the system as fermions at nonzero density coupled to a U(1) ChernSimons gauge field, we develope an effective theory via the technique of bosonization. The effective theory obtained this way contains an infinite tower of fields and is valid well beyond the cutoff for the effective field theory of the NambuGoldstone boson. It captures a much larger part of the spectrum, exhibiting multiple branches of gapped excitations as well as roton minima and maxima. 
Monday, March 15, 2021 10:12AM  10:24AM Live 
A46.00012: Fractional Chiral Hinge Insulator Nicolas Regnault, Anna Hackenbroich, Ana Hudomal, Norbert Schuch, Andrei B Bernevig We propose and study a wave function describing an interacting threedimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two noninteracting second order topological insulators with chiral hinge modes at half filling. We use variational Monte Carlo computations to characterize the model states via the entanglement entropy and chargespinfluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge c=1 and Luttinger parameter K=1/2, like the edge modes of a Laughlin 1/2 state. . A numerically pristine characterization of the bulk topology is provided by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host a twodimensional topological order with a TEE per surface compatible with half that of a Laughlin 1/2 state, a value that cannot be obtained from topological quantum field theory. 
Monday, March 15, 2021 10:24AM  10:36AM Live 
A46.00013: Induced superconductivity in a fractional quantum Hall edge Yuval Ronen, Onder Gul, Si Young Lee, Hassan Shapourian, Jonathan Zauberman, YoungHee Lee, Kenji Watanabe, Takashi Taniguchi, Ashvin Vishwanath, Amir Yacoby, Philip Kim In this talk, I will introduce highquality graphenebased van der Waals devices with narrow superconducting electrode (NbN), in which superconductivity and robust FQHE coexist. We find crossed Andreev reflection (CAR) across the superconductor separating two counterpropagating FQHE edges. Our observed CAR probability of the integer edges is insensitive to magnetic field, temperature, and filling, thereby providing evidence for spinorbit coupling inherited from NbN enabling the pairing of the otherwise spinpolarized edges. FQHE edges notably exhibit a CAR probability higher than that of integer edges once fully developed. This FQHE CAR probability remains nonzero down to our lowest accessible temperature, suggesting superconducting pairing of fractional charges. These results provide a route to realize novel topological superconducting phases with universal braiding statistics in FQHE–superconductor hybrid devices. 
Monday, March 15, 2021 10:36AM  10:48AM Live 
A46.00014: Extraction of manybody Chern number from a single wave function Hossein Dehghani, ZePei Cian, Mohammad Hafezi, Maissam Barkeshli The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the manybody Chern number. The conventional calculation of this invariant in interacting systems requires a family of manybody wave functions parameterized by twist angles in order to calculate the Berry curvature. In this paper, we demonstrate how to extract the Chern number given a single manybody wave function, without knowledge of the Hamiltonian. 
Monday, March 15, 2021 10:48AM  11:00AM Live 
A46.00015: The origin of multiple clustering behaviors in superconformal minimal models Yichen Hu, Jeffrey C. Y. Teo The bulkboundary correspondence is a robust and essential feature of many topological phases of matter which relates bulk wavefunctions to correlation functions of the edge conformal field theory. One prominent set of examples are the ReadRezayi series of quantum Hall states. Their wavefunctions (correlators in edge CFT) are well captured by Jack polynomials which encode clustering behaviors of particles approaching each other. In this work, we investigate wavefunctions of topological phases corresponding to the N=1 superconformal minimal model type. We present exact decompositions of supersymmetry generating operators into a sum of simpler operators with specific clustering behaviors. In this way, their 2npoint wavefunctions(correlators) can be computed from ground up using these building blocks. Our results provide an intuitive understanding of clustering behaviors and internal structures of these wavefunctions(correlators). Extensions to other superconformal minimal models are also discussed. 
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