Hierarchical fractional quantum Hall states, like that at filling fraction equal to 2/3, are believed to consist of several branches of chiral edge modes [Phys. Rev. Lett. 64, 220 (1990)]. In this picture, equilibration between edge modes is necessary to explain the universal (fractionally) quantized Hall conductance [Phys. Rev. Lett. 72, 4129 (1994)]. To probe this equilibration, we study out-of-time-ordered correlation functions in the theory for the 2/3 fractional quantum Hall edge. These correlation functions provide a diagnostic of chaotic behavior in classical systems. To study the interplay of these correlation functions with electrical transport, we calculate their dependence on (short-ranged) electron-electron interactions and the interaction with disorder.

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Hall viscosity is a nondissipative response function describing momentum transport in two-dimensional systems with broken parity. It is quantized in the quantum Hall regime, and contains information about the topological order of the quantum Hall state. Hall viscosity can distinguish different quantum Hall states with identical Hall conductances, but different topological order. To date, an experimentally accessible signature of Hall viscosity is lacking. We exploit the fact that Hall viscosity contributes to charge transport at finite wavelengths, and can therefore be extracted from nonlocal resistance measurements in inhomogeneous charge flows. We explain how to determine the Hall viscosity from such a transport experiment. In particular, we show that the profile of the electrochemical potential close to contacts where current is injected is sensitive to the value of the Hall viscosity.

We argue that a SO(d) magnetic monopole in an asymptotically AdS space-time is dual to a d-dimensional strongly coupled system in a solid state. We derive the quadratic action for the boundary phonons in the probe limit and show that, when the boundary conditions preserve conformal symmetry, the longitudinal and transverse sound speeds are related to each other as expected from effective field theory arguments. We then include backreaction and calculate the free energy of the solid for a particular choice of mixed boundary conditions, corresponding to a relevant multi-trace deformation of the boundary theory. We find that our solid undergoes a solid-to-liquid first order phase transition by melting into a Schwarzshild-AdS black hole as the temperature is raised.

We discuss the connection between loop models of particle-hole invariant theories of anyons to field theoretic dualities. We discuss systems defined both purely in two spatial dimensions and as boundaries of three dimensional systems, as well as the role of quantum anomalies. We comment on the significance of our results to theories of quantum phase transitions in fractional quantum Hall fluids and other two and three-dimensional topological fluids.

Understanding the structure of the wave-function has played an important role in understanding topological orders. Besides providing a way to construct simple exactly solvable models, it also connects the underlying mathematical framework with a physically intuitive picture. In this work, we present a wave-function approach for studying a large class of fracton phases. Fracton phases generically support excitations with restricted mobility and have a subextensive ground state degeneracy. We show that a large class of three-dimensional fracton phases can be understood as the condensation of extended objects, dubbed “cage-nets”. These highly fluctuating cage-nets provide a simple wave-function picture for understanding a class of discrete fracton states. We also construct two simple exactly solvable models in which the ground state wave-functions are cage-net condensates. These models support fractons and non-Abelian excitations that can only move in one- or two-dimensions. We further argue that the fractons will not carry any topological degeneracy in the construction employed in this work.

Although quantum Hall plateau transitions have been the prime examples of quantum criticality in a disordered electron system for the past three decades, many questions remain unanswered. Scaling of the measured electrical conductivity in the vicinity of these transitions reveals the surprising phenomenon of superuniversality where different transitions appear to share the same correlation length and dynamical critical exponent. Previous theoretical studies of these transitions within the framework of Abelian Chern-Simons theory coupled to matter found critical exponents that appear to directly depend on the change of the Hall conductivity across a specific phase transition, in contrast to what is observed experimentally. Here, we use non-Abelian bosonization and modular transformations to investigate theoretically the phenomenon of superuniversality. Specifically, we introduce a new effective theory that has an emergent U(N) gauge symmetry with N > 1 for a quantum phase transition between an integer quantum Hall state and an insulator. We then use modular transformations to generate from this theory new effective descriptions for transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have Abelian statistics. In the 't Hooft large N limit, the correlation length and dynamical critical exponents are independent of the particular transition. We argue that this superuniversality survives away from the large N limit using recent duality conjectures.

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We explain the lattice setup for studying QED_3 and we present some numerical results about QED_3 with single two-component massless Dirac fermion whose parity anomaly is cancelled by two infinite mass fermions of half the charge.

We discuss higher dimensional generalizations of the $0+1$-dimensional Sachdev-Ye-Kitaev (SYK) model. Unlike the previous constructions where multiple SYK copies would be coupled via some spatially short-ranged one and/or $q$-particle random hopping processes, this study focuses on algebraically varying long-range (spatially and/or temporally) correlated random couplings in $d+1$ dimensions. Such pertinent topics as translationally-invariant strong-coupling solutions, emergent reparametrization symmetry, effective action for fluctuations, and chaotic behavior (or a lack thereof) are addressed. We find that the most appealing properties of the original SYK model that suggest the existence of its $1+1$-dimensional holographic gravity dual do not survive the aforementioned generalizations, thus providing no further support for the hypothetical generalized holographic conjecture.

We propose a trial wave function for the quantum Hall bilayer system of total filling factor $\nu_T=1$ at a layer distance $d$ to magnetic length $\ell$ ratio $d/\ell=\kappa_{c1} \approx 1.1$, where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anti-composite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at $d/\ell=\kappa_{c1}$, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function and the ground state of a small size exact diagonalization is peaked near $d/\ell=\kappa_{c1}$, which supports our theory.

Fractons are quasiparticle excitations in d = 3 gapped topological ordered phases whose motion is constrained. It has been noticed that in the higher rank U(1) gauge theories, charges become fractons and cannot move freely due to the extra conservation laws. To make connection to the gapped fracton models, we study what happens when the higher rank gauge theories are Higgsed. Surprisingly, all the higher rank Z_N gauge theories obtained through Higgsing do not contain fractons. In particular, we show that the rank-2 Z_2 gauge theories are equivalent to several copies of Toric Codes while fracton appears when certain degrees of freedom of the gauge fields are frozen.

Numerical and experimental observations indicate that a particle-hole (PH) symmetry is realized by two-dimensional electrons that half-fill a Landau level. Prior work [Phys. Rev. B 95,23 (2017)] studied the implications of weakly broken PH symmetry on Weiss oscillations, a type of magnetoresistance oscillation, about half-filling using the Dirac composite fermion theory proposed by Son [Phys. Rev. X 5, 031027 (2015)]. Here, we extend this prior work by including the effects of fluctuations of the emergent gauge field that couples to the Dirac composite fermion. We compare our results to experiment and other composite fermions theories such as [Phys. Rev. B 47, 7312 (1993)] and [Phys. Rev. B 92,16 (2015)].

Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that Hall viscosity at zero frequency and momentum vanishes.

We study tight-binding models of interacting Majorana (Hermitian) modes on a one-dimensional chain and a square lattice. Using dual spin models in the strongly interacting regime, field theory and renormalization group in the weakly interacting regime, and several numerical methods, we find rich phase diagrams as a function of interaction strength. In 1D, we find a gapped supersymmetric region and a novel gapless phase with coexisting Luttinger liquid and Ising degrees of freedom. Three critical points occur: supersymmetric tricritical Ising, Lifshitz and a novel generalization of the commensurate-incommensurate transition. In 2D, we find several emergent symmetries, multiple broken symmetry phases, and a superfluid phase separated by a supersymmetric transition from a gapless normal phase.

The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this work, we focus on unitary transformations and show that matrix product operators that are unitary provides a necessary and sufficient representation of 1D unitaries that preserve locality. Moreover, we show that the matrix product representation gives a straight-forward way to extract the GNVW index defined in Ref.\cite{Gross2012} for classifying 1D locality preserving unitaries. The key to our discussion is a set of 'fixed point' conditions which characterize the form of the matrix product unitary operators after blocking sites. This work is closely related to classifying the boundary behavior of periodically-driven (Floquet) systems.

We formulate a Chern-Simons composite fermion theory for Fractional Chern Insulators (FCIs), whereby bare fermions are mapped into composite fermions coupled to a lattice Chern-Simons gauge theory. We apply this construction to a Chern insulator model on the kagome lattice and identify a rich structure of gapped topological phases characterized by fractionalized excitations including states with unequal filling and Hall conductance. Gapped states with the same Hall conductance at different filling fractions are characterized as realizing distinct symmetry fractionalization classes.

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We use holography to study a (1+1)-dimensional CFT coupled to an impurity. The CFT is an SU(N) gauge theory at large N, with strong gauge interactions. We demonstrate the Kondo effect, and calculate the impurity spectral functions and entanglement entropy. Our study provides an example in which the Kondo resonance survives strong correlations, and uncover a novel mechanism for generating Fano resonances, via a novel RG flows between (0+1)-dimensional fixed points.