arXiv subjects

Maissam Barkeshli

Publications and source records attributed to Maissam Barkeshli.

At least 73 records · Page 4Linked to original sources

arXiv2018

Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter

We study a class of anomalies associated with time-reversal and spatial reflection symmetry in (2+1)D topological phases of matter. In these systems, the topological quantum numbers of the quasiparticles, such as the fusion rules and braiding statistics, possess a $\mathbb{Z}_2$ symmetry which can be associated with either time-reversal (denoted $\mathbb{Z}_2^{\bf T})$ or spatial reflections. Under this symmetry, correlation functions of all Wilson loop operators in the low energy topological quantum field theory (TQFT) are invariant. However, the theories that we study possess a severe anomaly associated with the failure to consistently localize the symmetry action to the quasiparticles, precluding even defining a notion of symmetry fractionalization. We present simple sufficient conditions which determine when $\mathbb{Z}_2^{\bf T}$ symmetry localization anomalies exist. We present an infinite series of TQFTs with such anomalies, some examples of which include USp$(4)_2$ and SO$(4)_4$ Chern-Simons (CS) theory. The theories that we find with these $\mathbb{Z}_2^{\bf T}$ anomalies can be obtained by gauging the unitary $\mathbb{Z}_2$ subgroup of a different TQFT with a $\mathbb{Z}_4^{\bf T}$ symmetry. We show that the anomaly can be resolved in several ways: (1) the true symmetry of the theory is $\mathbb{Z}_4^{\bf T}$, or (2) the theory can be considered to be a theory of fermions, with ${\bf T}^2 = (-1)^{N_f}$ corresponding to fermion parity. Finally, we demonstrate that theories with the $\mathbb{Z}_2^{\bf T}$ localization anomaly can be compatible with $\mathbb{Z}_2^{\bf T}$ if they are "pseudo-realized" at the surface of a (3+1)D symmetry-enriched topological phase. The "pseudo-realization" refers to the fact that the bulk (3+1)D system is described by a dynamical $\mathbb{Z}_2$ gauge theory and thus only a subset of the quasiparticles are confined to the surface.

cond-mat.str-el↗

arXiv2018

The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories

We use the Higgs mechanism to investigate connections between higher-rank symmetric $U(1)$ gauge theories and gapped fracton phases. We define two classes of rank-2 symmetric $U(1)$ gauge theories: the $(m,n)$ scalar and vector charge theories, for integer $m$ and $n$, which respect the symmetry of the square (cubic) lattice in two (three) spatial dimensions. We further provide local lattice rotor models whose low energy dynamics are described by these theories. We then describe in detail the Higgs phases obtained when the $U(1)$ gauge symmetry is spontaneously broken to a discrete subgroup. A subset of the scalar charge theories indeed have X-cube fracton order as their Higgs phase, although we find that this can only occur if the continuum higher rank gauge theory breaks continuous spatial rotational symmetry. However, not all higher rank gauge theories have fractonic Higgs phases; other Higgs phases possess conventional topological order. Nevertheless, they yield interesting novel exactly solvable models of conventional topological order, somewhat reminiscent of the color code models in both two and three spatial dimensions. We also investigate phase transitions in these models and find a possible direct phase transition between four copies of $\mathbb{Z}_2$ gauge theory in three spatial dimensions and X-cube fracton order.

cond-mat.str-el↗

arXiv2018

Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics

We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then lead to a class of generalized Gauss law constraints. The charge and magnetic excitations in these theories have restricted, subdimensional dynamics, providing a generalization of recently studied higher-rank symmetric $U(1)$ gauge theories to the case where arbitrary spatial rotational symmetries are broken. These theories can describe situations where charges exist at the corners of fractal operators, thus providing a continuum effective field theoretic description of Haah's code and Yoshida's Sierpinski prism model. We also present a $3+1$-dimensional $U(1)$ theory that does not have a non-trivial discrete $\mathbb{Z}_p$ counterpart.

cond-mat.str-el↗

arXiv2018

Topological exciton Fermi surfaces in two-component fractional quantized Hall insulators

A wide variety of two-dimensional electron systems (2DES) allow for independent control of the total and relative charge density of two-component fractional quantum Hall (FQH) states. In particular, a recent experiment on bilayer graphene (BLG) observed a continuous transition between a compressible and incompressible phase at total filling $ν_T = \frac{1}{2}$ as charge is transferred between the layers, with the remarkable property that the incompressible phase has a finite interlayer polarizability. We argue that this occurs because the topological order of $ν_T = \frac{1}{2}$ systems supports a novel type of interlayer exciton that carries Fermi statistics. If the fermionic excitons are lower in energy than the conventional bosonic excitons (i.e., electron-hole pairs), they can form an emergent neutral Fermi surface, providing a possible explanation of an incompressible yet polarizable state at $ν_T = \frac{1}{2}$. We perform exact diagonalization studies which demonstrate that fermionic excitons are indeed lower in energy than bosonic excitons. This suggests that a "topological exciton metal" hidden inside a FQH insulator may have been realized experimentally in BLG. We discuss several detection schemes by which the topological exciton metal can be experimentally probed.

cond-mat.str-el↗

arXiv2017

Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface

The Lieb-Schultz-Mattis theorem and its higher dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases (SETs) with on-site unitary symmetries, enables us to develop a framework for understanding the structure of SETs with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling", which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing on-site symmetry protected degeneracies.

cond-mat.str-el↗

arXiv2017

Modular transformations through sequences of topological charge projections

The ground state subspace of a topological phase of matter forms a representation of the mapping class group of the space on which the state is defined. We show that elements of the mapping class group of a surface of genus $g$ can be obtained through a sequence of topological charge projections along at least three mutually intersecting non-contractible cycles. We demonstrate this both through the algebraic theory of anyons and also through an analysis of the topology of the space-time manifold. We combine this result with two observations: (i) that surfaces of genus $g$ can be effectively simulated in planar geometries by using bilayer, or doubled, versions of the topological phase of interest, and inducing the appropriate types of gapped boundaries; and (ii) that the required topological charge projections can be implemented as adiabatic unitary transformations by locally tuning microscopic parameters of the system, such as the energy gap. These observations suggest a possible path towards effectively implementing modular transformations in physical systems. In particular, they also show how the $\text{Ising} \otimes \overline{\text{Ising}}$ state, in the presence of disconnected gapped boundaries, can support universal topological quantum computation.

cond-mat.str-el↗

arXiv2016

Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies

We study symmetry-enriched topological (SET) phases in 2+1 space-time dimensions with spatial reflection and/or time-reversal symmetries. We provide a systematic construction of a wide class of reflection and time-reversal SET phases in terms of a topological path integral defined on general space-time manifolds. An important distinguishing feature of different topological phases with reflection and/or time-reversal symmetry is the value of the path integral on non-orientable space-time manifolds. We derive a simple general formula for the path integral on the manifold $Σ^2 \times S^1$, where $Σ^2$ is a two-dimensional non-orientable surface and $S^1$ is a circle. This also gives an expression for the ground state degeneracy of the SET on the surface $Σ^2$ that depends on the reflection symmetry fractionalization class, generalizing the Verlinde formula for ground state degeneracy on orientable surfaces. Consistency of the action of the mapping class group on non-orientable manifolds leads us to a constraint that can detect when a time-reversal or reflection SET phase is anomalous in (2+1)D and, thus, can only exist at the surface of a (3+1)D symmetry protected topological (SPT) state. Given a (2+1)D reflection and/or time-reversal SET phase, we further derive a general formula that determines which (3+1)D reflection and/or time-reversal SPT phase hosts the (2+1)D SET phase as its surface termination. A number of explicit examples are studied in detail.

cond-mat.str-el↗

arXiv2016

Charge $2e/3$ superconductivity and topological degeneracies without localized zero modes in bilayer fractional quantum Hall states

It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes. We focus mainly on electron-hole bilayers, with a $\pm 1/3$ Laughlin FQH state in each layer, with boundaries that are proximity-coupled to a superconductor. We show that the superconductor induces charge $2e/3$ quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (1) topologically protected degeneracies that can be measured through charge sensing experiments and (2) a fractional charge $2e/3$ AC Josephson effect. We demonstrate that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode. We discuss several practical advantages of this proposal over previous work, and also extensions to electron-electron bilayers at $ν= 2/3 + 1/3$ coupled to superconductivity, and to electron-hole bilayers with only interlayer tunneling.

cond-mat.str-el↗

arXiv2015

Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States

We show that the $ν=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a function of the relevant length scales, in spite of the presence of gapless excitations, including gapless fermions. These results are compatible with charge conservation, but do not require it. We discuss generalizations to other integer and fractional quantum Hall states, and classify possible mechanisms for appearance of Majorana zero modes at domain walls.

cond-mat.str-el↗

arXiv2015

Physical Architecture for a Universal Topological Quantum Computer based on a Network of Majorana Nanowires

The idea of topological quantum computation (TQC) is to store and manipulate quantum information in an intrinsically fault-tolerant manner by utilizing the physics of topologically ordered phases of matter. Currently, one of the most promising platforms for a topological qubit is in terms of Majorana fermion zero modes (MZMs) in spin-orbit coupled superconducting nanowires. However, the topologically robust operations that are possible with MZMs can be efficiently simulated on a classical computer and are therefore not sufficient for realizing a universal gate set for TQC. Here, we show that an array of coupled semiconductor-superconductor nanowires with MZM edge states can be used to realize a more sophisticated type of non-Abelian defect: a genon in an Ising $\times$ Ising topological state. This leads to a possible implementation of the missing topologically protected $π/8$ phase gate and thus universal TQC based on semiconductor-superconductor nanowire technology. We provide detailed numerical estimates of the relevant energy scales, which we show to lie within accessible ranges.

cond-mat.mes-hall↗

arXiv2015

Superconductivity Induced Topological Phase Transition at the Edge of Even Denominator Fractional Quantum Hall States

We show that every even-denominator fractional quantum Hall (FQH) state possesses at least two robust, topologically distinct gapless edge phases if charge conservation is broken at the boundary by coupling to a superconductor. The new edge phase allows for the possibility of a direct coupling between electrons and emergent neutral fermions of the FQH state. This can potentially be experimentally probed through geometric resonances in the tunneling density of states at the edge, providing a probe of fractionalized, yet electrically neutral, bulk quasiparticles. Other measurable consequences include a charge $e$ fractional Josephson effect, a charge $e/4q$ quasiparticle blocking effect in filling fraction $p/2q$ FQH states, and modified edge electron tunneling exponents.

cond-mat.str-el↗

arXiv2015

Abelian and Non-Abelian States in $ν=2/3$ Bilayer Fractional Quantum Hall Systems

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two- component FQH systems at total filling fraction $ν= n+ 2/3$, for integer $n$. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here, we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction $ν= n+2/3$, including in particular the possibility of the non-Abelian $Z_4$ parafermion state. In $ν= 2/3$ bilayers, we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the $Z_4$ state. On the other hand, in single-component systems at $ν= 8/3$, we find that the $Z_4$ parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed $ν= 8/3$ state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively.

cond-mat.str-el↗

arXiv2015

Particle-Hole Symmetry and the Composite Fermi Liquid

The half-filled Landau level is widely believed to be described by the Halperin-Lee-Read theory of the composite Fermi liquid (CFL). In this paper, we develop a theory for the particle-hole conjugate of the CFL, the Anti-CFL, which we argue to be a distinct phase of matter as compared with the CFL. The Anti-CFL provides a possible explanation of a recent experiment [Kamburov et. al., Phys. Rev. Lett. 113, 196801 (2014)] demonstrating that the density of composite fermions in GaAs quantum wells corresponds to the electron density when the filling fraction $ν< 1/2$ and to the hole density when $ν> 1/2$. We introduce a local field theory for the CFL and Anti-CFL in the presence of a boundary, which we use to study CFL - Insulator - CFL junctions, and the interface between the Anti-CFL and CFL. We show that the CFL - Anti-CFL interface allows partially fused boundary phases in which "composite electrons" can directly tunnel into "composite holes," providing a non-trivial example of transmutation between topologically distinct quasiparticles. We discuss several observable consequences of the Anti-CFL, including a predicted resistivity jump at a first order transition between uniform CFL and Anti-CFL phases. We also present a theory of a continuous quantum phase transition between the CFL and Anti-CFL. We conclude that particle-hole symmetry requires a modified view of the half-filled Landau level, in the presence of strong electron-electron interactions and weak disorder, as a critical point between the CFL and the Anti-CFL.

cond-mat.str-el↗

arXiv2014

Coherent Transmutation of Electrons into Fractionalized Anyons

Electrons have three quantized properties -- charge, spin, and Fermi statistics -- that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron as it enters certain exotic states of matter known as a quantum spin liquid (QSL). In a QSL, electron spins collectively form a highly entangled quantum state that gives rise to emergent gauge forces and fractionalization of spin, charge, and statistics. We show that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasiparticle, leaving its spin, charge, or statistics behind. We use these ideas to propose a number of universal, conclusive experimental signatures that would establish fractionalization in QSLs.

cond-mat.str-el↗

arXiv2014

Fibonacci Anyons From Abelian Bilayer Quantum Hall States

The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this paper, we consider a simple bilayer fractional quantum Hall (FQH) system with the $1/3$ Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous `Fibonacci'anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at $ν= 2/3$ in bilayers, as past experiments may not have definitively ruled them out.

cond-mat.str-el↗

arXiv2014

Generalized Kitaev Models and Slave Genons

We present a wide class of partially integrable lattice models with two-spin interactions, which generalize the Kitaev honeycomb model. These models have an infinite number of conserved quantities associated with each plaquette of the lattice, conserved large loop operators on the torus, and protected topological degeneracy. We introduce a `slave-genon' approach, which generalizes the Majorana fermion approach in the Kitaev honeycomb model. The Hilbert space of our spin model can be embedded into an enlarged Hilbert space of non-Abelian twist defects, referred to as genons. In the enlarged Hilbert space, the spin model is exactly reformulated as a model of non-Abelian genons coupled to a discrete gauge field. We discuss in detail a particular $Z_3$ generalization, and show that in a certain limit the model is analytically tractable and may produce a non-Abelian topological phase with chiral parafermion edge states.

cond-mat.str-el↗

arXiv2014

Experimental Proposal to Detect Topological Ground State Degeneracy

One of the most profound features of topologically ordered states of matter, such as the fractional quantum Hall (FQH) states, is that they possess topology-dependent ground state degeneracies that are robust to all local perturbations. Here we propose to directly detect these topological degeneracies in an experimentally accessible setup. The detection scheme uses electrical conductance measurements in a double layer FQH system with appropriately patterned top and bottom gates. We discuss two experimental platforms; in the first, the detection of topologically degenerate states coincides with the detection of $Z_N$ parafermion zero modes. We map the relevant physics to a single-channel $Z_N$ quantum impurity model, providing a novel generalization of the Kondo model. Our proposal can also be adapted to detect the $Z_N$ parafermion zero modes recently discovered in FQH line junctions proximitized with superconductivity.

cond-mat.str-el↗

arXiv2013

Non-Fermi liquids and the Wiedemann-Franz law

A general discussion of the ratio of thermal and electrical conductivities in non-Fermi liquid metals is given. In metals with sharp Drude peaks, the relevant physics is correctly organized around the slow relaxation of almost-conserved momenta. While in Fermi liquids both currents and momenta relax slowly, due to the weakness of interactions among low energy excitations, in strongly interacting non-Fermi liquids typically only momenta relax slowly. It follows that the conductivities of such non-Fermi liquids are obtained within a fundamentally different kinematics to Fermi liquids. Among these strongly interacting non-Fermi liquids we distinguish cases with only one almost-conserved momentum, which we term hydrodynamic metals, and with many patchwise almost-conserved momenta. For all these cases, we obtain universal expressions for the ratio of conductivities that violate the Wiedemann-Franz law. We further discuss the case in which long-lived `cold' quasiparticles, in general with unconventional scattering rates, coexist with strongly interacting hot spots, lines or bands. For these cases, we characterize circumstances under which non-Fermi liquid transport, in particular a linear in temperature resistivity, is and is not compatible with the Wiedemann-Franz law. We suggest the likely outcome of future transport experiments on CeCoIn5, YbRh2Si2 and Sr3Ru2O7 at their critical magnetic fields.

cond-mat.str-el↗