arXiv subjects

Ashvin Vishwanath

Publications and source records attributed to Ashvin Vishwanath.

At least 199 records · Page 11Linked to original sources

arXiv2016

Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories

The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions. As opposed to conventional Landau-Ginzburg-Wilson phases, which are classified on the basis of the spontaneous breaking of an underlying symmetry, topologically ordered phases, such as those occurring in the fractional quantum Hall effect, are absolutely stable, not requiring any such symmetry. Recently, though, it has been realized that symmetries, which may still be present in such systems, can give rise to a host of new, distinct, many-body phases, all of which share the same underlying topological order. A useful approach to classifying SETs is to determine all possible such symmetry actions on the anyons that are algebraically consistent with the anyons' statistics. Remarkably, however, there exist symmetry actions that, despite being algebraically consistent, cannot be realized in any physical system, and hence do not lead to valid 2d SETs. One class of such `anomalous' SETs, characterized by certain disallowed symmetry fractionalization patters, finds a physical interpretation as an allowed surface state of certain 3d short-range entangled phases, but another, characterized by some seemingly valid but anomalous permutation actions of the symmetry on the anyons, has so far eluded a physical interpretation. In this work, we find a physical realization for these anomalously permuting SETs as surface theories of certain 3d long-range entangled phases, completing our understanding of general anomalous SETs in 2 dimensions.

cond-mat.str-el↗

arXiv2016

Charged fermions coupled to $\mathbb{Z}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions

We consider a 2+1 dimensional model of charged fermions coupled to a $\mathbb{Z}_2$ gauge field, and study the confinement transition in this regime. To elucidate the phase diagram of this model, we introduce a method to handle the Gauss law constraint within sign problem free determinantal quantum Monte Carlo, at any charge density. For generic charge densities, $\mathbb{Z}_2$ gauge fluctuations mediate pairing and the ground state is a gapped superfluid. Superfluidity also appears in the confined phase. This is reminiscent of the BCS-BEC crossover, except that a true zero temperature transition occurs here, with the maximum $T_c$ achieved near the transition. At half-filling also one obtains a large Fermi surface which is gapped at zero temperature. However, on increasing fermion hopping a $π$-flux phase is spontaneously generated, with emergent Dirac fermions that are stable against pairing. In contrast to a Fermi liquid of electrons, the change in Fermi surface volumes of the $\mathbb{Z}_2$ fermions occurs without the breaking of translation symmetry. Unexpectedly, the numerics indicate a single continuous transition between the deconfined Dirac phase and the confined superfluid, in contrast to the naive expectation of a split transition, where a gap to fermions precedes confinement.

cond-mat.str-el↗

arXiv2016

Filling-Enforced Quantum Band Insulators in Spin-Orbit Coupled Crystals

While band insulators are usually described in wavevector space in terms of fully filled bands, they are sometimes also described in terms of a complementary Wannier picture in which electrons occupy localized, atom-like orbitals. Under what conditions does the latter picture break down? The presence of irremovable quantum entanglement between different sites can obstruct a localized orbital description, which occurs in systems like Chern and topological insulators. We collectively refer to such states as Quantum Band Insulators (QBIs). Here we report the theoretical discovery of a filling-enforced QBI - that is, a free electron insulator in which the band filling is smaller than the minimum number dictated by the atomic picture. Consequently such insulators have no representation in terms of filling localized orbitals and must be QBIs. This is shown to occur in models of certain cubic crystals with non-symmorphic space groups. Like topological insulators, filling-enforced QBIs require spin-orbit coupling. However, in contrast, they do not typically exhibit protected surface states. Instead their nontrivial nature is revealed by studying the quantum entanglement of their ground state wavefunction.

cond-mat.str-el↗

arXiv2016

Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids

We study 2+1 dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the action of symmetry, leading to symmetry enriched topological (SET) phases. Here we present a K-matrix Chern-Simons approach to identify all distinct phases with Abelian topological order, in the presence of unitary or anti-unitary global symmetries . A key step is the identification of an edge sewing condition that is used to check if two putative phases are indeed distinct. We illustrate this method for the case of $Z_2$ topological order ($Z_2$ spin liquids), in the presence of an internal Z$_2$ global symmetry. We find 6 distinct phases. The well known quantum number fractionalization patterns account for half of these states. Phases also differ due to the addition of a symmetry protected topological (SPT) phase. Also, we allow for the unconventional possibility that anyons are exchanged by the symmetry. This leads to 2 additional phases with symmetry protected Majorana edge modes. Other routes to realizing protected edge states in SET phases are identified. Symmetry enriched Laughlin states and double semion theories are also discussed. Two surprising lessons that emerge are: (i) gauging the global symmetry of distinct SET phases always lead to different topological orders with the same total quantum dimension, (ii) gauge theories with distinct Dijkgraaf-Witten topological terms may have the same topological order.

cond-mat.str-el↗

arXiv2016

Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals

We determine conditions on the filling of electrons in a crystalline lattice to obtain the equivalent of a band insulator -- a gapped insulator with neither symmetry breaking nor fractionalized excitations. We allow for strong interactions, which precludes a free particle description. Previous approaches that extend the Lieb-Schultz-Mattis argument invoked spin conservation in an essential way, and cannot be applied to the physically interesting case of spin-orbit coupled systems. Here we introduce two approaches, the first an entanglement based scheme, while the second studies the system on an appropriate flat `Bieberbach' manifold to obtain the filling conditions for all 230 space groups. These approaches only assume time reversal rather than spin rotation invariance. The results depend crucially on whether the crystal symmetry is symmorphic. Our results clarify when one may infer the existence of an exotic ground state based on the absence of order, and we point out applications to experimentally realized materials. Extensions to new situations involving purely spin models are also mentioned.

cond-mat.str-el↗

arXiv2015

Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals

We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools - semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals - we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically calculated quantum oscillations for generic Weyl semimetals with distinctly curved Fermi arcs on the two surfaces. Based on these methods, we identify a 'magic' magnetic-field angle where quantum oscillations become independent of sample thickness, with striking experimental implications. We also analyze the stability of these quantum oscillations to disorder, and show that the high-field oscillations are expected to persist in samples whose thickness parametrically exceeds the quantum mean free path.

cond-mat.mes-hall↗

arXiv2015

Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet

The anyonic excitations of a spin-liquid can feature fractional quantum numbers under space-group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in DMRG. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.

cond-mat.str-el↗

arXiv2015

A Quantum Dipolar Spin Liquid

Quantum spin liquids are a new class of magnetic ground state in which spins are quantum mechanically entangled over macroscopic scales. Motivated by recent advances in the control of polar molecules, we show that dipolar interactions between S=1/2 moments stabilize spin liquids on the triangular and kagome lattices. In the latter case, the moments spontaneously break time-reversal, forming a chiral spin liquid with robust edge modes and emergent semions. We propose a simple route toward synthesizing a dipolar Heisenberg antiferromagnet from lattice-trapped polar molecules using only a single pair of rotational states and a constant electric field.

cond-mat.str-el↗

arXiv2015

A bosonic topological phase in a paired superfluid

We study an effective model of two interacting species of bosons in two dimensions, which is amenable to sign problem free Monte Carlo simulations. In addition to conventional ground states, we access a paired superfluid which is also a topological phase, protected by the remaining $U(1) \times \mathbb{Z}_2$ symmetry. This phase arises from the condensation of a composite object, the bound state of vortices and anti-vortices of one species, to a boson of the second species. We introduce a bulk response function, the Ising analog of the quantized Hall effect, to diagnose the topological phase. The interplay of broken symmetry and topology leads to interesting effects such as fractionally charged vortices in the paired superfluid. Possible extensions towards realistic models of cold atomic bosons are discussed.

cond-mat.str-el↗

arXiv2015

Time reversal invariant gapped boundaries of the double semion state

The boundary of a fractionalized topological phase can be gapped by condensing a proper set of bosonic quasiparticles. Interestingly, in the presence of a global symmetry, such a boundary can have different symmetry transformation properties. Here we present an explicit example of this kind, in the double semion state with time reversal symmetry. We find two distinct cases where the semionic excitations on the boundary can transform either as time reversal singlets or as time reversal (Kramers) doublets, depending on the coherent phase factor of the Bose condensate. The existence of these two possibilities are demonstrated using both field theory argument and exactly solvable lattice models. Furthermore, we study the domain walls between these two types of gapped boundaries and find that the application of time reversal symmetry tunnels a semion between them.

cond-mat.str-el↗

arXiv2015

Many-body localization protected quantum state transfer

In thermal phases, the quantum coherence of individual degrees of freedom is rapidly lost to the environment. Many-body localized (MBL) phases limit the spread of this coherence and appear promising for quantum information applications. However, such applications require not just long coherence times but also a means to transport and manipulate information. We demonstrate that this can be done in a one dimensional model of interacting spins at infinite temperature. Our protocol utilizes protected qubits which emerge at the boundary between topological and trivial phases. State transfer occurs via dynamic shifts of this boundary and is shown to preserve quantum information. As an example, we discuss the implementation of a universal, two-qubit gate based upon MBL-protected quantum state transfer.

quant-ph↗

arXiv2015

The half-filled Landau level: the case for Dirac composite fermions

One of the most spectacular experimental findings in the fractional quantum Hall effect is evidence for an emergent Fermi surface when the electron density is nearly half the density of magnetic flux quanta ($ν= 1/2$). The seminal work of Halperin, Lee, and Read (HLR) first predicted that at $ν= 1/2$ composite fermions--bound states of an electron and a pair of vortices--experience zero net magnetic field and can form a "composite Fermi liquid" with an emergent Fermi surface. In this paper we use infinite cylinder DMRG to provide compelling numerical evidence for the existence of a Fermi sea of composite fermions for realistic interactions between electrons at $ν= 1/2$. Moreover, we show that the state is particle-hole symmetric, in contrast to the construction of HLR. Instead, our findings are consistent if the composite fermions are massless Dirac particles, at finite density, similar to the surface state of a 3D topological insulator. Exploiting this analogy we devise a numerical test and successfully observe the suppression of $2k_F$ backscattering characteristic of Dirac particles.

cond-mat.str-el↗

arXiv2015

Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order

We construct an exactly soluble Hamiltonian on the D=3 cubic lattice, whose ground state is a topological phase of bosons protected by time reversal symmetry, i.e a symmetry protected topological (SPT) phase. In this model anyonic excitations are shown to exist at the surface but not in the bulk. The statistics of these surface anyons is explicitly computed and shown to be identical to the 3-fermion Z2 model, a variant of Z2 topological order which cannot be realized in a purely D=2 system with time reversal symmetry. Thus the model realizes a novel surface termination for SPT phases, which only becomes available in D=3: that of a fully symmetric gapped surface with topological order. The 3D phase found here is also outside the group cohomology classification that appears to capture all SPT phases in lower dimensions. It is identified with a phase previously predicted from a field theoretic analysis, whose surface is roughly `half' of a Kitaev E8 phase. Our construction utilizes the Walker-Wang prescription to create a 3D confined phase with surface anyons,which can be extended to other symmetry classes and topological orders.

cond-mat.str-el↗

arXiv2015

Electric Field-Induced Skyrmion Crystals via Charged Monopoles in Insulating Helimagets

Electrons propagating in a magnetically ordered medium experience an additional gauge field associated with the Berry phase of their spin following the local magnetic texture. In contrast to the usual electromagnetic field, this gauge field admits monopole excitations, corresponding to hedgehog defects of the magnetic order. In an insulator, these hedgehogs carry a well-defined electric charge allowing for them to be controlled by electric fields. One particularly robust mechanism that contributes to the charge is the orbital magnetoelectric effect, captured by a $θ$ angle, which leads to a charge of $eθ/2π$ on hedgehogs. This is a direct consequence of the Witten effect for magnetic monopoles in a $θ$ medium. A physical consequence is that external electric fields can induce skyrmion crystal phases in insulating helimagnets.

cond-mat.str-el↗

arXiv2015

Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3

A family of insulating iridates with chemical formula Li$_2$IrO$_3$ has recently been discovered, featuring three distinct crystal structures $α,β,γ$ (honeycomb, hyperhoneycomb, stripyhoneycomb). Measurements on the three-dimensional polytypes, $β$- and $γ$-Li$_2$IrO$_3$, found that they magnetically order into remarkably similar spiral phases, exhibiting a non-coplanar counter-rotating spiral magnetic order with equivalent q=0.57 wavevectors. We examine magnetic Hamiltonians for this family and show that the same triplet of nearest-neighbor Kitaev-Heisenberg-Ising (KJI) interactions reproduces this spiral order on both $β,γ$-Li$_2$IrO$_3$ structures. We analyze the origin of this phenomenon by studying the model on a 1D zigzag chain, a structural unit common to the three polytypes. The zigzag-chain solution transparently shows how the Kitaev interaction stabilizes the counter-rotating spiral, which is shown to persist on restoring the inter-chain coupling. Our minimal model makes a concrete prediction for the magnetic order in $α$-Li$_2$IrO$_3$.

cond-mat.str-el↗

arXiv2015

Protection of topological order by symmetry and many-body localization

In closed quantum systems, strong randomness can localize many-body excitations, preventing ergodicity. An interesting consequence is that high energy excited states can exhibit quantum coherent properties, such as symmetry protected topological (SPT) order, that otherwise only occur in equilibrium ground states. Here, we ask: which types of SPT orders can be realized in highly excited states of a many-body (MB) localized system? We argue that this question is equivalent to whether an SPT order can be realized in an exactly solvable lattice model of commuting projectors. This perspective enables a sharp definition of MB localizability. Using this criterion, it is straightforward to establish that whereas all bosonic SPTs in spatial dimensions $d=1,\,2,\,3$ are MB localizable, chiral phases (e.g. quantum Hall fluids) are not. We also show that free fermion SPTs in $d >1$ (including topological insulators and superconductors) cannot be localized if interactions are weak. A key question is whether strong interactions can render them MB localizable, which we study in the context of a class of $d=2$ topological superconductors. Using a decorated domain wall (DDW) approach we show that some phases in this class are MB localizable, when they correspond to bosonic SPT orders. However, a similar DDW approach faces a fatal obstruction to realizing certain intrinsically fermionic SPT orders, an issue we argue may persist beyond this specific construction.

cond-mat.dis-nn↗

arXiv2015

Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators

Particle-vortex duality is a powerful theoretical tool that has been used to study bosonic systems. Here we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by a dual theory, QED3 with a dual Dirac fermion coupled to a gauge field. This duality is established by considering two alternate descriptions of the 3d topological insulator (TI) surface. The first description is the usual Dirac cone surface state. The second description is accessed via an electric-magnetic duality of the bulk TI coupled to a gauge field, which maps it to a gauged topological superconductor. This alternate description ultimately leads to a new surface theory - dual QED3. The dual theory provides an explicit derivation of the T-Pfaffian state, a proposed surface topological order of the TI, which is simply the paired superfluid state of the dual fermions. The roles of time reversal and particle-hole symmetry are exchanged by the duality, which connects some of our results to a recent conjecture by Son on particle-hole symmetric quantum Hall states.

cond-mat.str-el↗

arXiv2015

`Gauging' time reversal symmetry in tensor network states

It is well known that unitary symmetries can be `gauged', i.e. defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an anti-unitary symmetry. Here we discuss a route to gauging time reversal symmetry which applies to gapped quantum ground states that admit a tensor network representation. The tensor network representation of quantum states provides a notion of locality for the wave function coefficient and hence a notion of locality for the action of complex conjugation in anti-unitary symmetries. Based on that, we show how time reversal can be applied locally and also describe time reversal symmetry twists which act as gauge fluxes through nontrivial loops in the system. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain time reversal symmetric topological phases in $D=1,2$ are readily extracted using these ideas.

cond-mat.str-el↗