arXiv subjects

Ashvin Vishwanath

Publications and source records attributed to Ashvin Vishwanath.

At least 181 records · Page 10Linked to original sources

arXiv2017

Mean-field scaling of the superfluid to Mott insulator transition in a 2D optical superlattice

The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number $z$. We test this scaling directly by comparing coherence properties of $^{87}$Rb gases that are driven across the superfluid to Mott insulator transition within optical lattices of either the kagome ($z=4$) or the triangular ($z=6$) geometries. The coherent fraction measured for atoms in the kagome lattice is lower than for those in a triangular lattice with the same interaction and tunneling energies. A comparison of measurements from both lattices agrees quantitatively with the scaling prediction. We also study the response of the gas to a change in lattice geometry, and observe the dynamics as a strongly interacting kagome-lattice gas is suddenly "hole-doped" by introducing the additional sites of the triangular lattice.

cond-mat.quant-gas↗

arXiv2017

Discrete time crystals: rigidity, criticality, and realizations

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.

cond-mat.dis-nn↗

arXiv2017

An infinite family of 3d Floquet topological paramagnets

We uncover an infinite family of time-reversal symmetric 3d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium, and are governed by an infinite set of $Z_2$-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3d FTPMs are not captured by group cohomology methods, and cannot be obtained from equilibrium classifications simply by treating the discrete time-translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous $Z_2$ (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2d system without breaking time reversal symmetry.

cond-mat.str-el↗

arXiv2017

Symmetry-based Indicators of Band Topology in the 230 Space Groups

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.

cond-mat.str-el↗

arXiv2017

Floquet topological phases protected by time glide symmetry

We study Floquet topological phases in periodically driven systems that are protected by "time glide symmetry", a combination of reflection and half time period translation. Time glide symmetry is an analog of glide symmetry with partial time translation replacing the partial space translation, and hence, is an intrinsically dynamical symmetry which may be engineered in periodically driven systems by exploiting the controllability of driving. We present lattice models of time glide symmetric Floquet topological insulators in two and three dimensions. The topological numbers characterizing those Floquet topological phases are derived from the half period time evolution operator along with time glide operator. Moreover, we classify Floquet topological phases protected by time glide symmetry in general dimensions using a Clifford algebra approach. The obtained classification table is similar to that for topological crystalline insulators protected by static reflection symmetry, but shows nontrivial entries in different combination of symmetries, which clarifies that time glide symmetric Floquet topological phases are a distinct set of topological phases from topological crystalline insulators. We also classify Floquet topological phases with "time screw symmetry," defined as a two-fold spatial rotation accompanied by half-period time translation.

cond-mat.str-el↗

arXiv2017

Classification of Interacting Topological Floquet Phases in One Dimension

Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting fermionic and bosonic quantum systems subject to periodic driving, which we dub Floquet SPTs (FSPTs). For physical realizations of interacting FSPTs, many-body localization by disorder is a crucial ingredient, required to obtain a stable phase that does not catastrophically heat to infinite temperature. We demonstrate that bosonic and fermionic FSPTs phases are classified by the same criteria as equilibrium phases, but with an enlarged symmetry group $\tilde G$, that now includes discrete time translation symmetry associated with the Floquet evolution. In particular, 1D bosonic FSPTs are classified by projective representations of the enlarged symmetry group $H^2({\tilde G},U(1))$. We construct explicit lattice models for a variety of systems, and then formalize the classification to demonstrate the completeness of this construction. We also derive general constraints on localization and symmetry based on the representation theory of the symmetry group, and show that symmetry-preserving localized phases are possible only for Abelian symmetry groups. In particular, this rules out the possibility of many-body localized SPTs with continuous spin symmetry.

cond-mat.str-el↗

arXiv2017

Dyonic Lieb-Shultz-Mattis Theorem and Symmetry Protected Topological Phases in Decorated Dimer Models

We consider 2+1D lattice models of interacting bosons or spins, with both magnetic flux and fractional spin in the unit cell. We propose and prove a modified Lieb-Shultz Mattis (LSM) theorem in this setting, which applies even when the spin in the enlarged magnetic unit cell is integral. There are two nontrivial outcomes for gapped ground states that preserve all symmetries. In the first case, one necessarily obtains a symmetry protected topological (SPT) phase with protected edge states. This allows us to readily construct models of SPT states by decorating dimer models of Mott insulators to yield SPT phases, which should be useful in their physical realization. In the second case, exotic bulk excitations, i.e. topological order, is necessarily present. While both scenarios require fractional spin in the lattice unit cell, the second requires that the symmetries protecting the fractional spin is related to that involved in the magnetic translations. Our discussion encompasses the general notion of fractional spin (projective symmetry representations) and magnetic flux (magnetic translations tied to a symmetry generator). The resulting SPTs display a dyonic character in that they associate charge with symmetry flux, allowing the flux in the unit cell to screen the projective representation on the sites. We provide an explicit formula that encapsulates this physics, which identifies a specific set of allowed SPT phases.

cond-mat.str-el↗

arXiv2017

Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices

We study the ground states of 2D lattice bosons in an artificial gauge field. Using state of the art DMRG simulations we obtain the zero temperature phase diagram for hardcore bosons at densities $n_b$ with flux $n_ϕ$ per unit cell, which determines a filling $ν=n_b/n_ϕ$. We find several robust quantum Hall phases, including (i) a bosonic integer quantum Hall phase (BIQH) at $ν=2$, that realizes an interacting symmetry protected topological phase in 2D (ii) bosonic fractional quantum Hall phases including robust states at $ν=2/3$ and a Laughlin state at $ν=1/2$. The observed states correspond to the bosonic Jain sequence ($ν=p/(p+1)$) pointing towards an underlying composite fermion picture. In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation beginning from independent chains, and ramping up interchain couplings. Using time dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. Besides the wave-function overlap, we utilize a simple physical signature of these phases, the non-monotonic behavior of a two-point correlation, a direct consequence of edge states in a finite system, to numerically assess the effectiveness of the preparation scheme. Our proposal only utilizes existing experimental capabilities.

cond-mat.str-el↗

arXiv2017

Interacting invariants for Floquet phases of fermions in two dimensions

We construct a many-body quantized invariant that sharply distinguishes among two dimensional non-equilibrium driven phases of interacting fermions. This is an interacting generalization of a band-structure Floquet quasi-energy winding number, and describes chiral pumping of quantum information along the edge. In particular, our invariant sharply distinguishes between a trivial and anomalous Floquet Anderson insulator in the interacting, many-body localized setting. It also applies more generally to models where only fermion parity is conserved, where it differentiates between trivial models and ones that pump Kitaev Majorana chains to the boundary, such as ones recently introduced in the context of emergent fermions arising from eigenstate $\Z_2$ topological order. We evaluate our invariant for the edge of such a system with eigenstate $\Z_2$ topological order, and show that it is necessarily nonzero when the Floquet unitary exchanges electric and magnetic excitations, proving a connection between bulk anyonic symmetry and edge chirality.

cond-mat.str-el↗

arXiv2017

Topological Materials Discovery using Electron Filling Constraints

Nodal semimetals, materials systems with nodal-point or -line Fermi surfaces, are much sought after for their novel transport and topological properties. Identification of experimental materials candidates, however, has mainly relied on exhaustive database searches. Here we show how recent studies on the interplay between electron filling and nonsymmorphic space-group symmetries can guide the search for nodal semimetals which are `filling-enforced'. We recast the previously-derived constraints on the allowed electron fillings for band insulators in the 230 space groups into a new form, which enables effective screening of materials candidates based solely on their (1) space group, (2) electron count in the formula unit, and (3) multiplicity of the formula unit. This criterion greatly reduces the computation load for discovering topological materials in a database of previously-synthesized compounds. Of the more than 30,000 entires listed in a few selected nonsymmorphic space groups, our filling criterion alone eliminates 96% of the entries before they are passed on for further analysis. From this guided search, we discover a handful of candidates, including the monoclinic crystals Ca$_2$Pt$_2$Ga, AgF$_2$, and Ca$_2$InOsO$_6$, and the orthorhombic crystal CsHg$_2$. Based on ab initio calculations, we show that these materials have filling-enforced Dirac nodes near the Fermi energy. In addition, we also identify CaPtGa as a promising filling-enforced Dirac-ring semimetal candidate.

cond-mat.mtrl-sci↗

arXiv2017

Phonon analogue of topological nodal semimetals

Topological band structures in electronic systems like topological insulators and semimetals give rise to highly unusual physical properties. Analogous topological effects have also been discussed in bosonic systems, but the novel phenomena typically occur only when the system is excited by finite-frequency probes. A mapping recently proposed by Kane and Lubensky [Nat. Phys. 10, 39 (2014)], however, establishes a closer correspondence. It relates the zero-frequency excitations of mechanical systems to topological zero modes of fermions that appear at the edges of an otherwise gapped system. Here we generalize the mapping to systems with an intrinsically gapless bulk. In particular, we construct mechanical counterparts of topological semimetals. The resulting gapless bulk modes are physically distinct from the usual acoustic Goldstone phonons, and appear even in the absence of continuous translation invariance. Moreover, the zero-frequency phonon modes feature adjustable momenta and are topologically protected as long as the lattice coordination is unchanged. Such protected soft modes with tunable wavevector may be useful in designing mechanical structures with fault-tolerant properties.

cond-mat.mes-hall↗

arXiv2016

Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work we study the effect of a space dependent Weyl node separation, which we interpret as an emergent background axial vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or non-uniform magnetization and can also be engineered in cold-atomic systems. Using a semiclassical approach we show that the resulting axial magnetic field $\mathbf{B}_{5}$ is observable through an enhancement of the conductivity as $σ\sim \mathbf{B}_{5} ^{2}$ due to an underlying chiral pseudo magnetic effect. We then use two lattice models to analyze the effect of $\mathbf{B}_5$ on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau level structure for different spatial profiles of $\mathbf{B}_5$, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as $n=0$ pseudo-Landau levels resulting from a $\mathbf{B}_5$ confined to the surface (ii) as a consequence of position-momentum locking a bulk $\mathbf{B}_5$ creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces and (iii) there are equilibrium bound currents proportional to $\mathbf{B}_{5}$ that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

cond-mat.mes-hall↗

arXiv2016

Superconductivity and Nematic Fluctuations in a model of FeSe monolayers: A Determinant Quantum Monte Carlo Study

In contrast to bulk FeSe, which exhibits nematic order and low temperature superconductivity, atomic layers of FeSe reverse the situation, having high temperature superconductivity appearing alongside a suppression of nematic order. To investigate this phenomenon, we study a minimal electronic model of FeSe, with interactions that enhance nematic fluctuations. This model is sign problem free, and is simulated using determinant quantum Monte Carlo (DQMC). We developed a DQMC algorithm with parallel tempering, which proves to be an efficient source of global updates and allows us to access the region of strong interactions. Over a wide range of intermediate couplings, we observe superconductivity with an extended s-wave order parameter, along with enhanced, but short ranged, $q=(0,0)$ ferro-orbital (nematic) order. These results are consistent with approximate weak coupling treatments that predict that nematic fluctuations lead to superconducting pairing. Surprisingly, in the parameter range under study, we do not observe nematic long range order. Instead, at stronger coupling an unusual insulating phase with $q=(π,π)$ antiferro-orbital order appears, which is missed by weak coupling approximations.

cond-mat.supr-con↗

arXiv2016

Duality and bosonization of (2+1)d Majorana fermions

We construct a dual bosonized description of a massless Majorana fermion in $(2+1)d$. In contrast to Dirac fermions, for which a bosonized description can be constructed using a flux attachment procedure, neutral Majorana fermions call for a different approach. We argue that the dual theory is an $SO(N)_1$ Chern-Simons gauge theory with a critical $SO(N)$ vector bosonic matter field ($N \geq 3$). The monopole of the $SO(N)$ gauge field is identified with the Majorana fermion. We provide evidence for the duality by establishing the correspondence of adjacent gapped phases and by a parton construction. We also propose a generalization of the duality to $N_f$ flavors of Majorana fermions, and discuss possible resolutions of a caveat associated with an emergent global $Z_2$ symmetry. Finally, we conjecture a dual description of an $\mathcal{N} = 1$ supersymmetric fixed point in $(2+1)d$, which is realized by tuning a single flavor of Majorana fermions to an interacting (Gross-Neveu) critical point.

cond-mat.str-el↗

arXiv2016

Chiral Floquet Phases of Many-body Localized Bosons

We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL) in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry, and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models, and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.

cond-mat.dis-nn↗

arXiv2016

Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level

The half filled Landau level is expected to be approximately particle-hole symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of the compressible state observed at this filling. Recent work indicates that, when particle-hole symmetry is preserved, the composite Fermions experience a quantized $π$-Berry phase upon winding around the composite Fermi-surface, analogous to Dirac fermions at the surface of a 3D topological insulator. In contrast, the effective low energy theory of the composite fermion liquid originally proposed by HLR lacks particle-hole symmetry and has vanishing Berry phase. In this paper, we explain how thermoelectric transport measurements can be used to test the Dirac nature of the composite Fermions by quantitatively extracting this Berry phase. First we point out that longitudinal thermopower (Seebeck effect) is non-vanishing due to the unusual nature of particle hole symmetry in this context and is not sensitive to the Berry phase. In contrast, we find that off-diagonal thermopower (Nernst effect) is directly related to the topological structure of the composite Fermi surface, vanishing for zero Berry phase and taking its maximal value for $π$ Berry phase. In contrast, in purely electrical transport signatures the Berry phase contributions appear as small corrections to a large background signal, making the Nernst effect a promising diagnostic of the Dirac nature of composite fermions.

cond-mat.str-el↗

arXiv2016

Transport evidence for Fermi-arc mediated chirality transfer in the Dirac semimetal Cd$_3$As$_2$

Dirac semi-metals show a linear electronic dispersion in three dimension described by two copies of the Weyl equation, a theoretical description of massless relativistic fermions. At the surface of a crystal, the breakdown of fermion chirality is expected to produce topological surface states without any counterparts in high-energy physics nor conventional condensed matter systems, the so-called "Fermi Arcs". Here we present Shubnikov-de Haas oscillations involving the Fermi Arc states in Focused Ion Beam prepared microstructures of Cd$_3$As$_2$. Their unusual magnetic field periodicity and dependence on sample thickness can be well explained by recent theoretical work predicting novel quantum paths weaving the Fermi Arcs together with chiral bulk states, forming "Weyl orbits". In contrast to conventional cyclotron orbits, these are governed by the chiral bulk dynamics rather than the common momentum transfer due to the Lorentz force. Our observations provide evidence for direct access to the topological properties of charge in a transport experiment, a first step towards their potential application.

cond-mat.mes-hall↗

arXiv2016

Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups

Nonsymmorphic symmetries like screws and glides produce electron band touchings, obstructing the formation of a band insulator and leading, instead, to metals or nodal semimetals even when the number of electrons in the unit cell is an even integer. Here, we calculate the electron fillings compatible with being a band insulator for all 230 space groups, for noninteracting electrons with time-reversal symmetry. Our bounds are tight - that is, we can rigorously eliminate band insulators at any forbidden filling and produce explicit models for all allowed fillings - and stronger than those recently established for interacting systems. These results provide simple criteria that should help guide the search for topological semimetals and, also, have implications for both the nature and stability of the resulting nodal Fermi surfaces.

cond-mat.str-el↗