arXiv subjects

Sarang Gopalakrishnan

Publications and source records attributed to Sarang Gopalakrishnan.

At least 127 records · Page 7Linked to original sources

arXiv2021

Stability of superdiffusion in nearly integrable spin chains

Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with nonabelian global symmetries. Superdiffusion is caused by giant Goldstone-like quasiparticles stabilized by integrability. Here, we argue that these giant quasiparticles remain long-lived, and give divergent contributions to the low-frequency conductivity $σ(ω)$, even in systems that are not perfectly integrable. We find, perturbatively, that $ σ(ω) \sim ω^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $σ(ω) \sim | \log ω|$ for noisy perturbations. The (presumable) crossover to regular diffusion appears to lie beyond low-order perturbation theory. By contrast, integrability-breaking perturbations that break the nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.

cond-mat.stat-mech↗

arXiv2021

Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, it was recently conjectured to also describe spin transport in the one-dimensional quantum Heisenberg model. We test this conjecture by experimentally probing transport in a cold-atom quantum simulator via the relaxation of domain walls in spin chains of up to 50 spins. We find that domain-wall relaxation is indeed governed by the KPZ dynamical exponent $z = 3/2$, and that the occurrence of KPZ scaling requires both integrability and a non-abelian SU(2) symmetry. Finally, we leverage the single-spin-sensitive detection enabled by the quantum-gas microscope to measure a novel observable based on spin-transport statistics, which yields a clear signature of the non-linearity that is a hallmark of KPZ universality.

cond-mat.quant-gas↗

arXiv2021

Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found in unitary models, those that occur here are \emph{incommensurate} with the drive frequency. The period of the incommensurate time-crystal phase may be tuned by adjusting the circuit parameters. We demonstrate that the phases of our quantum circuit, including the inherently non-equilibrium dynamical ones, correspond to complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model.

cond-mat.stat-mech↗

arXiv2021

Hydrodynamics of nonintegrable systems from a relaxation-time approximation

We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is based on a generalized relaxation-time approximation; it gives a simple, but surprisingly accurate, prescription for computing nonequilibrium transport even in strongly interacting systems. This approximation reproduces the crossover from generalized to conventional hydrodynamics in interacting one-dimensional Bose gases with integrability-breaking perturbations, both with and without momentum conservation. It also predicts the hydrodynamics of chaotic quantum spin chains, in good agreement with matrix product operator calculations.

cond-mat.stat-mech↗

arXiv2021

Lifetimes of local excitations in disordered dipolar quantum systems

When a strongly disordered system of interacting quantum dipoles is locally excited, the excitation relaxes on some (potentially very long) timescale. We analyze this relaxation process, both for electron glasses with strong Coulomb interactions - in which particle-hole dipoles are emergent excitations - and for systems (e.g., quantum magnets or ultracold dipolar molecules) made up of microscopic dipoles. We consider both energy relaxation rates ($T_1$ times) and dephasing rates ($T_2$ times), and their dependence on frequency, temperature, and polarization. Systems in both two and three dimensions are considered, along with the dimensional crossover in quasi-two dimensional geometries. A rich set of scaling laws is found.

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↗

arXiv2021

Local integrals of motion and the quasiperiodic many-body localization transition

We study the many body localization (MBL) transition for interacting fermions subject to quasiperiodic potentials by constructing the local integrals of motion (LIOMs) in the MBL phase as time-averaged local operators. We study numerically how these time-averaged operators evolve across the MBL transition. We find that the norm of such time-averaged operators drops discontinuously to zero across the transition; as we discuss, this implies that LIOMs abruptly become unstable at some critical localization length of order unity. We analyze the LIOMs using hydrodynamic projections and isolating the part of the operator that is associated with interactions. Equipped with this data we perform a finite-size scaling analysis of the quasiperiodic MBL transition. Our results suggest that the quasiperiodic MBL transition occurs at considerably stronger quasiperiodic modulations, and has a larger correlation-length critical exponent, than previous studies had found.

cond-mat.dis-nn↗

arXiv2020

Asymptotically exact theory for nonlinear spectroscopy of random quantum magnets

We study nonlinear response in quantum spin systems {near infinite-randomness critical points}. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in such systems. {We present exact results for nonlinear response in the 1D random transverse-field Ising model, from which we extract information about critical behavior that is absent in linear response. Our analysis yields exact scaling forms for the distribution functions of relaxation times that result from realistic channels for dissipation in random magnets}. We argue that our results capture the scaling of relaxation times and nonlinear response in generic random quantum magnets in any spatial dimension.

cond-mat.dis-nn↗

arXiv2020

Entanglement and purification transitions in non-Hermitian quantum mechanics

A quantum system subject to continuous measurement and post-selection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non-Hermitian Hamiltonian undergoes a spectral phase transition. On one side of this phase transition (for weak post-selection) an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions.

quant-ph↗

arXiv2020

Superuniversality of superdiffusion

Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-abelian global symmetry. This work offers a comprehensive group-theoretic account of this elusive phenomenon. For an integrable quantum model invariant under a global non-abelian simple Lie group $G$, we find that finite-temperature transport of Noether charges associated with symmetry $G$ in thermal states that are invariant under $G$ is universally superdiffusive and characterized by dynamical exponent $z = 3/2$. This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: we accordingly dub it as superuniversal. The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations. We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters. We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua. Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.

cond-mat.stat-mech↗

arXiv2020

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, that are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles. We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is sub-ballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via $x\sim t^{2/3}$) along both lines and at the $SO(4)$-symmetric point where they intersect. Our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

cond-mat.stat-mech↗

arXiv2020

Enhancing associative memory recall and storage capacity using confocal cavity QED

We introduce a near-term experimental platform for realizing an associative memory. It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity. The associative memory is realized by a confocal cavity QED neural network, with the cavity modes serving as the synapses, connecting a network of superradiant atomic spin ensembles, which serve as the neurons. Memories are encoded in the connectivity matrix between the spins, and can be accessed through the input and output of patterns of light. Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms. Our scheme has two conceptually novel elements. First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin-glass regime as a physical parameter is tuned---the positions of ensembles within the cavity. Second, and more importantly, the spins relax via deterministic steepest-descent dynamics, rather than Glauber dynamics. We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network's ability to store and recall memories beyond that of the standard Hopfield model. Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase. Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible.

quant-ph↗

arXiv2020

Quantum criticality in the 2d quasiperiodic Potts model

Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic $q$-state Potts model in $2+1d$. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of $q$, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be $ν=1$, saturating a modified version of the Harris-Luck criterion.

cond-mat.dis-nn↗

arXiv2020

Superdiffusion from emergent classical solitons in quantum spin chains

Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant quasiparticles" that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.

cond-mat.stat-mech↗

arXiv2020

Observation of a marginal Fermi glass using THz 2D coherent spectroscopy

A longstanding open problem in condensed matter physics is whether or not a strongly disordered interacting insulator can be mapped to a system of effectively non-interacting localized excitations. We investigate this issue on the insulating side of the 3D metal-insulator transition (MIT) in phosphorus doped silicon using the new technique of terahertz two dimensional coherent spectroscopy. Despite the intrinsically disordered nature of these materials, we observe coherent excitations and strong photon echoes that provide us with a powerful method for the study of their decay processes. We extract the first measurements of energy relaxation ($T_1$) and decoherence ($T_2$) times close to the MIT in this classic system. We observe that (i) both relaxation rates are linear in excitation frequency with a slope close to unity, (ii) the energy relaxation timescale $T_1$ counterintuitively increases with increasing temperature and (iii) the coherence relaxation timescale $T_2$ has little temperature dependence between 5 K and 25 K, but counterintuitively increases as the material is doped towards the MIT. We argue that these features imply that (a) the system behaves as a well isolated electronic system on the timescales of interest, and (b) relaxation is controlled by electron-electron interactions. We discuss the potential relaxation channels that may explain the behavior. Our observations constitute a qualitatively new phenomenology, driven by the interplay of strong disorder and strong electron-electron interactions, which we dub the marginal Fermi glass.

cond-mat.str-el↗

arXiv2020

Creating quantum many-body scars through topological pumping of a 1D dipolar gas

Quantum many-body scars, long-lived excited states of correlated quantum chaotic systems that evade thermalization, are of great fundamental and technological interest. We create novel scar states in a bosonic 1D quantum gas of dysprosium by stabilizing a super-Tonks-Girardeau gas against collapse and thermalization with repulsive long-range dipolar interactions. Stiffness and energy density measurements show that the system is dynamically stable regardless of contact interaction strength. This enables us to cycle contact interactions from weakly to strongly repulsive, then strongly attractive, and finally weakly attractive. We show that this cycle is an energy-space topological pump (due to a quantum holonomy). Iterating this cycle offers an unexplored topological pumping method to create a hierarchy of quantum many-body scar states.

cond-mat.quant-gas↗

arXiv2020

Critical properties of the measurement-induced transition in random quantum circuits

We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate $p_c = 0.17(1)$. We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the surface order parameter exponent appear different from that for stabilizer circuits or percolation, but we are unable to definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies $S_n$ depends strongly on the Rényi index $n$; for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite-size effects. We discuss how our numerical estimates constrain theories of the transition.

cond-mat.dis-nn↗

arXiv2020

Diffusive hydrodynamics from integrability breaking

We describe the crossover from generalized hydrodynamics to conventional hydrodynamics in nearly integrable systems. Integrable systems have infinitely many conserved quantities, which spread ballistically in general. When integrability is broken, only a few of these conserved quantities survive. The remaining conserved quantities are generically transported diffusively; we derive a compact and general diffusion equation for these. The diffusion constant depends on the matrix elements of the integrability-breaking perturbation; for a certain class of integrability-breaking perturbations, including long-range interactions, the diffusion constant can be expressed entirely in terms of generalized hydrodynamic data.

cond-mat.stat-mech↗