arXiv subjects

Sarang Gopalakrishnan

Publications and source records attributed to Sarang Gopalakrishnan.

At least 163 records · Page 9Linked to original sources

arXiv2018

Operator growth and eigenstate entanglement in an interacting integrable Floquet system

We analyze a simple model of quantum dynamics, which is a discrete-time deterministic version of the Frederickson-Andersen model. We argue that this model is integrable, with a quasiparticle description related to the classical hard-rod gas. Despite the integrability of the model, commutators of physical operators grow as in generic chaotic models, with a diffusively broadening front, and local operators obey the eigenstate thermalization hypothesis (ETH). However, large subsystems violate ETH; as a function of subsystem size, eigenstate entanglement first increases linearly and then saturates at a scale that is parametrically smaller than half the system size.

cond-mat.stat-mech↗

arXiv2018

Thermalization near integrability in a dipolar quantum Newton's cradle

Isolated quantum many-body systems with integrable dynamics generically do not thermalize when taken far from equilibrium. As one perturbs such systems away from the integrable point, thermalization sets in, but the nature of the crossover from integrable to thermalizing behavior is an unresolved and actively discussed question. We explore this question by studying the dynamics of the momentum distribution function in a dipolar quantum Newton's cradle consisting of highly magnetic dysprosium atoms. This is accomplished by creating the first one-dimensional Bose gas with strong magnetic dipole-dipole interactions. These interactions provide tunability of both the strength of the integrability-breaking perturbation and the nature of the near-integrable dynamics. We provide the first experimental evidence that thermalization close to a strongly interacting integrable point occurs in two steps: prethermalization followed by near-exponential thermalization. Exact numerical calculations on a two-rung lattice model yield a similar two-timescale process, suggesting that this is generic in strongly interacting near-integrable models. Moreover, the measured thermalization rate is consistent with a parameter-free theoretical estimate, based on identifying the types of collisions that dominate thermalization. By providing tunability between regimes of integrable and nonintegrable dynamics, our work sheds light both on the mechanisms by which isolated quantum many-body systems thermalize, and on the temporal structure of the onset of thermalization.

cond-mat.quant-gas↗

arXiv2018

Facilitated quantum cellular automata as simple models with nonthermal eigenstates and dynamics

We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a Floquet unitary. The dynamics of the models we discuss can be classically simulated, and their eigenstates classically constructed (although they are highly entangled). We consider a variety of models in both one and two dimensions, involving Clifford gates and Toffoli gates. For some of these models, we explicitly construct conserved densities; thus these models are "integrable." The other models do not seem to be integrable; yet, for some system sizes and boundary conditions, their eigenstate entanglement is strongly subthermal. Some of the models have exponentially many eigenstates in which one or more sites are "disentangled" from the rest of the system, as a consequence of reflection symmetry.

cond-mat.stat-mech↗

arXiv2018

Weyl semimetal to metal phase transitions driven by quasiperiodic potentials

We explore the stability of three-dimensional Weyl and Dirac semimetals subject to quasiperiodic potentials. We present numerical evidence that the semimetal is stable for weak quasiperiodic potentials, despite being unstable for weak random potentials. As the quasiperiodic potential strength increases, the semimetal transitions to a metal, then to an "inverted" semimetal, and then finally to a metal again. The semimetal and metal are distinguished by the density of states at the Weyl point, as well as by level statistics, transport, and the momentum-space structure of eigenstates near the Weyl point. The critical properties of the transitions in quasiperiodic systems differ from those in random systems: we do not find a clear critical scaling regime in energy; instead, at the quasiperiodic transitions, the density of states appears to jump abruptly (and discontinuously to within our resolution).

cond-mat.dis-nn↗

arXiv2017

Self-dual quasiperiodic systems with power-law hopping

We introduce and explore a family of self-dual models of single-particle motion in quasiperiodic potentials, with hopping amplitudes that fall off as a power law with exponent $p$. These models are generalizations of the familiar Aubry-Andre model. For large enough $p$, their static properties are similar to those of the Aubry-Andre model, although the low-frequency conductivity in the localized phase is sensitive to $p$. For $p \leq 2.1$ the Aubry-Andre localization transition splits into three transitions; two distinct intermediate regimes with both localized and delocalized states appear near the self-dual point of the Aubry-Andre model. In the intermediate regimes, the density of states is singular continuous in much of the spectrum, and is approximately self-similar: states form narrow energy bands, which are divided into yet narrower sub-bands; we find no clear sign of a mobility edge. When $p < 1$, localized states are not stable in random potentials; in the present model, however, tightly localized states are present for relatively large systems. We discuss the frequency-dependence and strong sample-to-sample fluctuations of the low-frequency optical conductivity, although a suitably generalized version of Mott's law is recovered when the power-law is slowly decaying. We present evidence that many of these features persist in models that are away from self-duality.

cond-mat.dis-nn↗

arXiv2017

Noise-induced subdiffusion in strongly localized quantum systems

We consider the dynamics of strongly localized systems subject to dephasing noise with arbitrary correlation time. Although noise inevitably induces delocalization, transport in the noise-induced delocalized phase is subdiffusive in a parametrically large intermediate-time window. We argue for this intermediate-time subdiffusive regime both analytically and using numerical simulations on single-particle localized systems. Furthermore, we show that normal diffusion is restored in the long-time limit, through processes analogous to variable-range hopping. With numerical simulations based on Lanczos exact diagonalization, we demonstrate that our qualitative conclusions are also valid for interacting systems in the many-body localized phase.

cond-mat.dis-nn↗

arXiv2017

Intertwined and vestigial order with ultracold atoms in multiple cavity modes

Atoms in transversely pumped optical cavities "self-organize" by forming a density wave and emitting superradiantly into the cavity mode(s). For a single-mode cavity, the properties of this self-organization transition are well characterized both theoretically and experimentally. Here, we explore the self-organization of a Bose-Einstein condensate in the presence of two cavity modes---a system that was recently experimentally realized [Leonard \emph{et al.}, \emph{Nature} {\bf 543}, 87 (2017)]. We argue that this system can exhibit a "vestigially ordered" phase in which neither cavity mode exhibits superradiance but the cavity modes are mutually phase-locked by the atoms. We argue that this vestigially ordered phase should generically be present in multimode cavity geometries.

cond-mat.quant-gas↗

arXiv2017

Rare region effects and dynamics near the many-body localization transition

The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally "in the other phase", i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local "baths" and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

cond-mat.dis-nn↗

arXiv2017

Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems

In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down completely, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge both for experiments and theory. Here, we experimentally explore the relaxation dynamics of an interacting gas of fermionic potassium atoms loaded in a two-dimensional optical lattice with different quasi-periodic potentials along the two directions. We observe a dramatic slowing down of the relaxation for intermediate disorder strengths and attribute this partially to configurational rare-region effects. Beyond a critical disorder strength, we see negligible relaxation on experimentally accessible timescales, indicating a possible transition into a two-dimensional MBL phase. Our experiments reveal a distinct interplay of interactions, disorder, and dimensionality and provide insights into regimes where controlled theoretical approaches are scarce.

cond-mat.quant-gas↗

arXiv2016

Adiabatic Quantum Search in Open Systems

Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size, their robustness in open systems remains unresolved. We study the dynamics in the proximity of such an avoided level crossing associated with the adiabatic quantum search algorithm in a quantum system that is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. At finite temperature, however, scattering processes render the algorithm inefficient and no quantum speedup can be achieved. Owing to the generic nature of our model, we expect our results to be widely applicable to other adiabatic quantum algorithms.

quant-ph↗

arXiv2016

Non-Fermi glasses: fractionalizing electrons at finite energy density

Non-Fermi liquids are metals that cannot be adiabatically deformed into free fermion states. We argue for the existence of "non-Fermi glasses," which are phases of interacting disordered fermions that are fully many-body localized, yet cannot be deformed into an Anderson insulator without an eigenstate phase transition. We explore the properties of such non-Fermi glasses, focusing on a specific solvable example. At high temperature, non-Fermi glasses have qualitatively similar spectral features to Anderson insulators. We identify a diagnostic, based on ratios of correlation functions, that sharply distinguishes between the two phases even at infinite temperature. We argue that our results and diagnostic should generically apply to the high-temperature behavior of the many-body localized descendants of fractionalized phases.

cond-mat.dis-nn↗

arXiv2016

Rare-Region Onset of Superconductivity in Granular Systems

The critical behavior of disordered systems-from metals (1) to magnets (2) and superconductors (3)-is often dominated by the behavior of rare regions of a correlated phase, which control the inception and dynamics of the phase transition. Yet, despite significant theoretical (3,4,5) and experimental (6,7,8,9) interest, there has been little direct evidence of the presence of these regions, or of their role in initiating transitions. Here, we provide direct evidence for rare-region effects at the onset of superconductivity in granular superconducting islands. By considering the strong diameter-dependence of the transition, as well as observations of large fluctuations in the transition temperature as island diameters decrease, we are able to show that superconducting order first appears in unusually large grains- i.e. rare regions- within each island and, due to proximity coupling, spreads to other grains. This work thus provides a quantitative, local understanding of the onset of correlated order in strongly disordered systems.

cond-mat.supr-con↗

arXiv2016

General theory of many body localized systems coupled to baths

We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of `boundary MBL' and `boundary baths').

cond-mat.dis-nn↗

arXiv2016

Griffiths effects and slow dynamics in nearly many-body localized systems

The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or "in the other phase". It is known that, in one dimension, these rare regions can cause the d.c. conductivity and diffusion constant to vanish even inside the delocalized thermal phase. Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wavevector-dependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.

cond-mat.dis-nn↗

arXiv2016

Regimes of heating and dynamical response in driven many-body localized systems

We explore the response of many-body localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinite-temperature generalization of the effective "heating rate" in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power-law of time. We discuss the mechanisms underlying this crossover in the MBL phase, and comment on its implications for the subdiffusive thermal phase near the MBL transition.

cond-mat.dis-nn↗

arXiv2016

Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid'" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long timescales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy are neither charge nor spin excitations, but neutral "phonon" modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.

cond-mat.dis-nn↗

arXiv2015

Prethermal Floquet Steady States and Instabilities in the Periodically Driven, Weakly Interacting Bose-Hubbard Model

We explore prethermal Floquet steady states and instabilities of the weakly interacting two-dimensional Bose-Hubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weak-coupling conserving approximation. We establish the regimes in which conventional (zero-momentum) and unconventional [$(π,π)$-momentum] condensates are stable on intermediate time scales. We find that condensate stability is \emph{enhanced} by increasing the drive strength, because this decreases the bandwidth of quasiparticle excitations and thus impedes resonant absorption and heating. Our results are directly relevant to a number of current experiments with ultracold bosons.

cond-mat.quant-gas↗

arXiv2015

Quantum Control of Many-body Localized States

We propose and analyze a new approach to the coherent control and manipulation of quantum degrees of freedom in disordered, interacting systems in the many-body localized phase. Our approach leverages a number of unique features of many-body localization: a lack of thermalization, a locally gapped spectrum, and slow dephasing. Using the technique of quantum phase estimation, we demonstrate a protocol that enables the local preparation of a many-body system into an effective eigenstate. This leads to the ability to encode information and control interactions without full microscopic knowledge of the underlying Hamiltonian. Finally, we analyze the effects of weak coupling to an external bath and provide an estimate for the fidelity of our protocol.

quant-ph↗