arXiv subjects

Vedika Khemani

Publications and source records attributed to Vedika Khemani.

At least 55 records · Page 3Linked to original sources

arXiv2021

Tri-unitary quantum circuits

We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in $(1+1)$-dimensional spacetime -- the two light cone edges, $δx=\pm vδt$, and the static worldline $δx=0$. Along these directions, correlation functions are obtained exactly in terms of quantum channels built from the individual gates that make up the circuit. We prove that, for a class of initial states, entanglement grows at the maximum allowed speed up to an entropy density of at least one half of the thermal value, at which point it becomes model-dependent. Finally, we extend our circuit construction to $2+1$ dimensions, where two-point correlation functions are confined to the one-dimensional edges of a tetrahedral light cone -- a subdimensional propagation of information reminiscent of "fractonic" physics.

quant-ph↗

arXiv2021

Many-body physics in the NISQ era: quantum programming a discrete time crystal

Recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices represents an exciting opportunity for many-body physics, by introducing new laboratory platforms with unprecedented control and measurement capabilities. We explore the implications of NISQ platforms for many-body physics in a practical sense: we ask which {\it physical phenomena}, in the domain of quantum statistical mechanics, they may realize more readily than traditional experimental platforms. As a particularly well-suited target, we identify discrete time crystals (DTCs), novel non-equilibrium states of matter that break time translation symmetry. These can only be realized in the intrinsically out-of-equilibrium setting of periodically driven quantum systems stabilized by disorder induced many-body localization. While precursors of the DTC have been observed across a variety of experimental platforms - ranging from trapped ions to nitrogen vacancy centers to NMR crystals - none have \emph{all} the necessary ingredients for realizing a fully-fledged incarnation of this phase, and for detecting its signature long-range \emph{spatiotemporal order}. We show that a new generation of quantum simulators can be programmed to realize the DTC phase and to experimentally detect its dynamical properties, a task requiring extensive capabilities for programmability, initialization and read-out. Specifically, the architecture of Google's Sycamore processor is a remarkably close match for the task at hand. We also discuss the effects of environmental decoherence, and how they can be distinguished from `internal' decoherence coming from closed-system thermalization dynamics. Already with existing technology and noise levels, we find that DTC spatiotemporal order would be observable over hundreds of periods, with parametric improvements to come as the hardware advances.

cond-mat.dis-nn↗

arXiv2021

A comment on "Discrete time crystals: rigidity, criticality, and realizations"

The Letter by N. Y. Yao et. al. [1,2] presents three models for realizing a many-body localized discrete time-crystal (MBL DTC): a short-ranged model [1], its revised version [2], as well as a long-range model of a trapped ion experiment [1,3]. We show that none of these realize an MBL DTC for the parameter ranges quoted in Refs. [1,2]. The central phase diagrams in [1] therefore cannot be reproduced. The models show rapid decay of oscillations from generic initial states, in sharp contrast to the robust period doubling dynamics characteristic of an MBL DTC. Long-lived oscillations from special initial states (such as polarized states) can be understood from the familiar low-temperature physics of a static transverse field Ising model, rather than the nonequilibrium physics of an eigenstate-ordered MBL DTC. Our results on the long-range model also demonstrate, by extension, the absence of an MBL DTC in the trapped ion experiment of Ref. [3].

cond-mat.dis-nn↗

arXiv2021

Entanglement phase transitions in measurement-only dynamics

Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This motivates us to introduce \emph{measurement-only models}, in which the "scrambling" and "un-scrambling" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. This represents a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is \emph{frustration}, or mutual incompatibility, of the measurements. Suprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local ($\gtrsim 3$-body) operators. We identify a class of exceptions to this behavior ("bipartite ensembles") which cannot sustain an entangling phase, but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light-cone, despite the non-locality inherent to quantum measurements.

quant-ph↗

arXiv2020

Topological and symmetry-enriched random quantum critical points

We study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogues of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of such symmetry-enriched random quantum spin chains. We uncover a new class of symmetry-enriched infinite randomness fixed points: while local bulk properties are indistinguishable from conventional random singlet phases, nonlocal observables and boundary critical behavior are controlled by a different renormalization group fixed point. We also illustrate how such new quantum critical points emerge naturally in Floquet systems.

cond-mat.str-el↗

arXiv2020

Postselection-free entanglement dynamics via spacetime duality

The dynamics of entanglement in `hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply \emph{postselection} on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of \emph{spacetime duality}. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics.

cond-mat.dis-nn↗

arXiv2020

From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras

We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with `spectrum generating algebras' that can be used to lift the degeneracy of the scar states and promote them to equally spaced `towers'. Our framework applies to several known models with scars, but we also introduce new models with scars that transform as irreducible representations of symmetries such as SU(3) and $q$-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present new examples of generalized AKLT models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-like models into our framework.

cond-mat.stat-mech↗

arXiv2020

Prethermalization without temperature

While a clean driven system generically absorbs energy until it reaches `infinite temperature', it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for non-trivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localised cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al., [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.

cond-mat.dis-nn↗

arXiv2020

Asymmetric butterfly velocities in 2-local Hamiltonians

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a "butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

cond-mat.stat-mech↗

arXiv2020

Perturbative instability towards delocalization at phase transitions between MBL phases

We examine the stability of marginally Anderson localized phase transitions between localized phases to the addition of many-body interactions, focusing in particular on the spin-glass to paramagnet transition in a disordered transverse field Ising model in one dimension. We find evidence for a perturbative instability of localization at finite energy densities once interactions are added, i.e. evidence for the relevance of interactions - in a renormalization group sense - to the non-interacting critical point governed by infinite randomness scaling. We introduce a novel diagnostic, the "susceptibility of entanglement", which allows us to perturbatively probe the effect of adding interactions on the entanglement properties of eigenstates, and helps us elucidate the resonant processes that can cause thermalization. The susceptibility serves as a much more sensitive probe, and its divergence can detect the perturbative beginnings of an incipient instability even in regimes and system sizes for which conventional diagnostics point towards localization. We expect this new measure to be of independent interest for analyzing the stability of localization in a variety of different settings.

cond-mat.dis-nn↗

arXiv2020

Kinetically constrained freezing transition in a dipole-conserving system

We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.

cond-mat.stat-mech↗

arXiv2020

Floquet prethermalization in a Bose-Hubbard system

Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prethermal' regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems.

cond-mat.quant-gas↗

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

Local constraints can globally shatter Hilbert space: a new route to quantum information protection

We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a "fractonic circuit" - a model of quantum circuit dynamics in one dimension constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic circuit dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. A large number of the emergent subsectors, exponentially many in the size of the system, have dimension one and exhibit strictly localized quantum dynamics---even in the absence of spatial disorder and in the presence of temporal noise. Exponentially large localized subspaces can be proven to exist for any one dimensional fractonic circuit with finite spatial range, and provide a potentially new route for the robust storage of quantum information. Other emergent subsectors display non-trivial dynamics and may be constructed by embedding finite sized non-trivial blocks into the localized subspace. The shattering of a particular symmetry sector into a distribution of dynamical subsectors with varying sizes leads to the coexistence of high and low entanglement states, i.e. this provides a general mechanism for the production of quantum many body scars. We discuss the detailed pattern of fracturing and its implications. We also discuss other mechanisms for similarly shattering Hilbert space.

cond-mat.stat-mech↗

arXiv2019

Signatures of integrability in the dynamics of Rydberg-blockaded chains

A recent experiment on a 51-atom Rydberg blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this article, we show that the experimental Hamiltonian exhibits non-thermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The unconventional quench dynamics in the parent model could signal a novel class of integrable system.

cond-mat.str-el↗

arXiv2018

Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in non-integrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models.

cond-mat.stat-mech↗

arXiv2018

Asymmetric butterfly velocities in Hamiltonian and circuit models

The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered commutators). In general, this velocity can depend on the direction of spreading and, indeed, the asymmetry between different directions can be made arbitrarily large using arbitrarily deep quantum circuits. Nevertheless, in almost all examples of local time-independent Hamiltonians that have been examined thus far, this velocity is independent of the direction of information propagation. In this work, we present two models with asymmetric $v_B$. The first is a time-independent Hamiltonian in one dimension with local, 3-site interactions. The second is a class of local unitary circuits, which we call $n$-staircases, where $n$ serves as a tunable parameter interpolating from $n=1$ with symmetric spreading to $n=\infty$ with completely chiral information propagation.

cond-mat.stat-mech↗