arXiv subjects

S. L. Sondhi

Publications and source records attributed to S. L. Sondhi.

At least 55 records · Page 3Linked to original sources

arXiv2020

Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions"

In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly problematic: they are unrealizable ${\it and}$ they violate well established principles for defining phases of matter. Indeed with infinite body operators allowed, almost all quantum systems are time crystals. In addition, one of their models is highly unstable and another amounts to isolating, via fine tuning, a single degree of freedom in a many body system--allowing for this elevates the pendulum of Galileo and Huygens to a genuine time crystal.

cond-mat.str-el↗

arXiv2019

A Brief History of Time Crystals

The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization. Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics --- that of an intrinsically out-of-equilibrium many-body phase of matter. We include a compendium of necessary background, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. We formalize the notion of a time-crystal as a stable, macroscopic, conservative clock --- explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. We also cover a range of related phenomena, including various types of long-lived prethermal time-crystals, and expose the roles played by symmetries -- exact and (emergent) approximate -- and their breaking. We clarify the distinctions between many-body time-crystals and other ostensibly similar phenomena dating as far back as the works of Faraday and Mathieu. En route, we encounter Wilczek's suggestion that macroscopic systems should exhibit TTSB in their ground states, together with a theorem ruling this out. We also analyze pioneering recent experiments detecting signatures of time crystallinity in a variety of different platforms, and provide a detailed theoretical explanation of the physics in each case. In all existing experiments, the system does not realize a `true' time-crystal phase, and we identify necessary ingredients for improvements in future experiments.

cond-mat.str-el↗

arXiv2019

Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunnelling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $ν$ of the underlying (integer) quantum Hall states. For $ν=1$ and in the absence of impurity scattering we argue that the wall hosts a single-channel Luttinger liquid whose gaplessness is a consequence of valley and charge conservation. For $ν=2$, it supports a two-channel Luttinger liquid, which for sufficiently strong interactions enters a symmetry-preserving thermal metal phase with a charge gap coexisting with gapless neutral intervalley modes. The domain wall physics in this state is identical to that of a bosonic topological insulator protected by $U(1)\times U(1)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these `anomalous' one-dimensional systems.

cond-mat.str-el↗

arXiv2019

Twisted bilayer graphene in a parallel magnetic field

We study the effect of an in-plane magnetic field on the non-interacting dispersion of twisted bilayer graphene. Our analysis is rooted in the chirally symmetric continuum model, whose zero-field band structure hosts exactly flat bands and large energy gaps at the magic angles. At the first magic angle, the central bands respond to a parallel field by forming a quadratic band crossing point (QBCP) at the Moire Brillouin zone center. Over a large range of fields, the dispersion is invariant with an overall scale set by the magnetic field strength. For deviations from the magic angle and for realistic interlayer couplings, the motion and merging of the Dirac points lying near charge neutrality are discussed in the context of the symmetries, and we show that small magnetic fields are able to induce a qualitative change in the energy spectrum. We conclude with a discussion on the possible ramifications of our study to the interacting ground states of twisted bilayer graphene systems.

cond-mat.str-el↗

arXiv2019

An Extension of ETH to Non-Equilibrium Steady States

We extend the notion of the Eigenstate Thermalization Hypothesis (ETH) to Open Quantum Systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation. We present evidence that the eigenstates of non-equilibrium steady state (NESS) density matrices obey a generalization of ETH in boundary-driven systems when the bulk Hamiltonian is non-integrable, just as eigenstates of Gibbs density matrices are conjectured to do in equilibrium. This generalized ETH, which we call NESS-ETH, can be used to obtain representative pure states that reproduce the expectation values of few-body operators in the NESS. The density matrices of these representative pure states can be further interpreted as weak solutions of the GKLS Master Equation. Additionally, we explore the validity and breakdown of NESS-ETH in the presence of symmetries, integrability and many-body localization in the bulk Hamiltonian.

cond-mat.stat-mech↗

arXiv2019

Topology and Broken Symmetry in Floquet Systems

Floquet systems are governed by periodic, time-dependent, Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However this unhappy state of affairs can be avoided in many ways. Instead, as has become clear from much recent work, they can exhibit a variety of nontrivial behavior---some of it impossible in undriven systems. In this review we describe the main ideas and themes of this work: novel Floquet drives which exhibit nontrivial topology in single-particle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of many-body Floquet phases and arguments for their stability to heating.

cond-mat.str-el↗

arXiv2019

Fractonic Chern-Simons and BF theories

Fracton order is an intriguing new type of order which shares many common features with topological order, such as topology-dependent ground state degeneracies, and excitations with mutual statistics. However, it also has several distinctive geometrical aspects, such as excitations with restricted mobility, which naturally lead to effective descriptions in terms of higher rank gauge fields. In this paper, we investigate possible effective field theories for 3D fracton order, by presenting a general philosophy whereby topological-like actions for such higher-rank gauge fields can be constructed. Our approach draws inspiration from Chern-Simons and BF theories in 2+1 dimensions, and imposes constraints binding higher-rank gauge charge to higher-rank gauge flux. We show that the resulting fractonic Chern-Simons and BF theories reproduce many of the interesting features of their familiar 2D cousins. We analyze one example of the resulting fractonic Chern-Simons theory in detail, and show that upon quantization it realizes a gapped fracton order with quasiparticle excitations that are mobile only along a sub-set of 1-dimensional lines, and display a form of fractional self-statistics. The ground state degeneracy of this theory is both topology- and geometry- dependent, scaling exponentially with the linear system size when the model is placed on a 3-dimensional torus. By studying the resulting quantum theory on the lattice, we show that it describes a $\mathbb{Z}_s$ generalization of the Chamon code.

cond-mat.str-el↗

arXiv2019

Operator Spreading in Quantum Maps

Operators in ergodic spin-chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin-chains. Here we initiate the study of "operator spreading" in quantum maps on a torus, systems which do not have a tensor-product Hilbert space or a notion of spatial locality. Using the perturbed Arnold cat map as an example, we analytically compare and contrast the evolutions of functions on classical phase space and quantum operator evolutions, and identify distinct timescales that characterize the dynamics of operators in quantum chaotic maps. Until an Ehrenfest time, the quantum system exhibits classical chaos, i.e. it mimics the behavior of the corresponding classical system. After an operator scrambling time, the operator looks "random" in the initial basis, a characteristic feature of quantum chaos. These timescales can be related to the quasi-energy spectrum of the unitary via the spectral form factor. Furthermore, we show examples of "emergent classicality" in quantum problems far away from the classical limit. Finally, we study operator evolution in non-chaotic and mixed quantum maps using the Chirikov standard map as an example.

cond-mat.stat-mech↗

arXiv2019

Interacting multi-channel topological boundary modes in a quantum Hall valley system

Symmetry and topology play key roles in the identification of phases of matter and their properties. Both concepts are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties. Domain walls between distinct broken symmetry QHFM phases are predicted to host gapless one-dimensional (1D) modes that emerge due to a topological change of the underlying electronic wavefunctions at such interfaces. Although a variety of QHFMs have been identified in different materials, probing interacting electronic modes at these domain walls has not yet been accomplished. Here we use a scanning tunneling microscope (STM) to directly visualize the spontaneous formation of boundary modes, within a sign-changing topological gap, at domain walls between different valley-polarized quantum Hall phases on the surface of bismuth. By changing the valley occupation and the corresponding number of modes at the domain wall, we can realize different regimes where the valley-polarized channels are either metallic or develop a spectroscopic gap. This behavior is a consequence of Coulomb interactions constrained by the symmetry-breaking valley flavor, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting Luttinger liquids.

cond-mat.mes-hall↗

arXiv2018

Fractal Symmetric Phases of Matter

We study spin systems which exhibit symmetries that act on a fractal subset of sites, with fractal structures generated by linear cellular automata. In addition to the trivial symmetric paramagnet and spontaneously symmetry broken phases, we construct additional fractal symmetry protected topological (FSPT) phases via a decorated defect approach. Such phases have edges along which fractal symmetries are realized projectively, leading to a symmetry protected degeneracy along the edge. Isolated excitations above the ground state are symmetry protected fractons, which cannot be moved without breaking the symmetry. In 3D, our construction leads additionally to FSPT phases protected by higher form fractal symmetries and fracton topologically ordered phases enriched by the additional fractal symmetries.

cond-mat.str-el↗

arXiv2018

Mott, Floquet, and the response of periodically driven Anderson insulators

We consider periodically driven Anderson insulators. The short time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times---which is the physics of Floquet late time states---and strong electric fields. This results in a `phase diagram' in the frequency-field strength plane, in which we identify four distinct regimes. These are: a linear response regime dominated by pre-existing Mott resonances, which exists provided Floquet saturation is not reached within a period; a non-linear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to pre-existing resonances; and finally an enhanced dissipative regime.

cond-mat.dis-nn↗

arXiv2018

Cooling arbitrary near-critical systems using hyperbolic quenches

We describe a quench protocol that allows the rapid preparation of ground states of arbitrary interacting conformal field theories in $1+1$ dimensions. We start from the ground state of a related gapped relativistic quantum field theory and consider sudden quenches along the space-like trajectories $t^2 - x^2 = T^2_0$ (parameterized by $T_0$) to a conformal field theory. Using only arguments of symmetry and conformal invariance, we show that the post-quench stress-energy tensor of the conformal field theory is uniquely constrained up to an overall scaling factor. Crucially, the $\textit{geometry}$ of the quench necessitates that the system approach the vacuum energy density over all space except the singular lines $x = \pm t$. The above arguments are verified using an exact treatment of the quench for the Gaussian scalar field theory (equivalently, the Luttinger liquid), and numerically for the quantum $O(N)$ model in the large-$N$ limit. Additionally, for the Gaussian theory, we find in fact that even when starting from certain excited states, the quench conserves entropy, and is thus also suitable for rapidly preparing excited states. Our methods serve as a fast, alternative route to reservoir-based cooling to prepare quantum states of interest.

cond-mat.stat-mech↗

arXiv2018

Symmetric Fracton Matter: Twisted and Enriched

In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that these can realize subsystem symmetry protected topological phases with gapless boundary modes. Gauging the planar subsystem symmetry leads to a fracton order in which particles restricted to move along lines exhibit a new type of statistical interaction that is specific to the lattice geometry. We show that both the gapless boundary modes of the ungauged theory, and the statistical interactions after gauging, are naturally captured by a higher-rank version of Chern-Simons theory. We also show that gauging only part of the subsystem symmetry can lead to symmetry-enriched fracton orders, with quasiparticles carrying fractional symmetry charge.

cond-mat.str-el↗

arXiv2018

Symmetry breaking and localization in a random Schwinger model with commensuration

We numerically investigate a lattice regularized version of quantum electrodynamics in one spatial dimension (Schwinger model). We work at a density where lattice commensuration effects are important, and preclude analytic solution of the problem by bosonization. We therefore numerically investigate the interplay of confinement, lattice commensuration, and disorder, in the form of a random chemical potential. We begin by pointing out that the ground state at commensurate filling spontaneously breaks the translational symmetry of the lattice. This feature is absent in the conventional lattice regularization, which breaks the relevant symmetry explicitly, but is present in an alternative (symmetric) regularization that we introduce. Remarkably, the spontaneous symmetry breaking survives the addition of a random chemical potential (which explicitly breaks the relevant symmetry) in apparent contradiction of the Imry-Ma theorem, which forbids symmetry breaking in one dimension with this kind of disorder. We identify the long range interaction as the key ingredient enabling the system to evade Imry-Ma constraints. We examine spatially resolved energy level statistics for the disordered system, and demonstrate that the low energy Hilbert space exhibits ergodicity breaking, with level statistics that fail to follow random matrix theory. A careful examination of the structure of low lying excited states reveals that disorder induced localization is responsible for the deviations from random matrix theory, and further reveals that the elementary excitations are charge neutral, and therefore not long range interacting.

cond-mat.str-el↗

arXiv2018

Subsystem symmetry protected topological order

In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry groups for such systems exhibit a macroscopic number of generators in the infinite volume limit. We construct a set of exactly solvable models in $2d$ and $3d$ which exhibit such subsystem SPT (SSPT) phases with one dimensional subsystem symmetries. These phases exhibit analogs of phenomena seen in SPTs protected by global symmetries: gapless edge modes, projective realizations of the symmetries at the edge and non-local order parameters. Such SSPT phases are proximate, in theory space, to previously studied phases that break the subsystem symmetries and phases with fracton order which result upon gauging them.

cond-mat.str-el↗

arXiv2018

Correlation function diagnostics for type-I fracton phases

Fracton phases are recent entrants to the roster of topological phases in three dimensions. They are characterized by subextensively divergent topological degeneracy and excitations that are constrained to move along lower dimensional subspaces, including the eponymous fractons that are immobile in isolation. We develop correlation function diagnostics to characterize Type I fracton phases which build on their exhibiting {\it partial deconfinement}. These are inspired by similar diagnostics from standard gauge theories and utilize a generalized gauging procedure that links fracton phases to classical Ising models with subsystem symmetries. En route, we explicitly construct the spacetime partition function for the plaquette Ising model which, under such gauging, maps into the X-cube fracton topological phase. We numerically verify our results for this model via Monte Carlo calculations.

cond-mat.str-el↗

arXiv2017

Fast preparation of critical ground states using superluminal fronts

We propose a spatio-temporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally-moving `front' that $\textit{locally}$ quenches the mass, leaves behind it (in space) a state $\textit{arbitrarily close}$ to the ground state of the gapless model. Importantly, our protocol takes time $\mathcal{O} \left( L \right)$ to produce the ground state of a system of size $\sim L^d$ ($d$ spatial dimensions), while a fully adiabatic protocol requires time $\sim \mathcal{O} \left( L^2 \right)$ to produce a state with exponential accuracy in $L$. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof-of-concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in $d = 1$. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin-chain.

cond-mat.quant-gas↗

arXiv2017

Evidence of a fractional quantum Hall nematic phase in a microscopic model

At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family of anisotropic Laughlin states as trial wave functions, we find a continuous quantum phase transition between the isotropic Laughlin liquid and the FQH nematic. Results of numerical exact diagonalization also suggest that rotational symmetry is spontaneously broken, and that the phase diagram of the model contains both a nematic and a stripe phase.

cond-mat.str-el↗