Showing papers by "Shivaji Lal Sondhi published in 2017"
TL;DR: In this paper, the authors show that the spreading of operators in random circuits is described by a hydrodynamical equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (eg, no conserved energy).
Abstract: Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory and holography We tackle this problem in 1D spin-chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs), and entanglement growth in this setting These results follow from the observation that the spreading of operators in random circuits is described by a `hydrodynamical' equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (eg, no conserved energy) In this hydrodynamic picture quantum information travels in a front with a `butterfly velocity' $v_{\text{B}}$ that is smaller than the light cone velocity of the system, while the front itself broadens diffusively in time The OTOC increases sharply after the arrival of the light cone, but we do \emph{not} observe a prolonged exponential regime of the form $\sim e^{\lambda_\text{L}(t-x/v)}$ for a fixed Lyapunov exponent $\lambda_\text{L}$ We find that the diffusive broadening of the front has important consequences for entanglement growth, leading to an entanglement velocity that can be significantly smaller than the butterfly velocity We conjecture that the hydrodynamical description applies to more generic ergodic systems and support this by verifying numerically that the diffusive broadening of the operator wavefront also holds in a more traditional non-random Floquet spin-chain We also compare our results to Clifford circuits, which have less rich hydrodynamics and consequently trivial OTOC behavior, but which can nevertheless exhibit linear entanglement growth and thermalization
297 citations
TL;DR: In the past decade, remarkable progress in the physics of closed quantum systems away from equilibrium, culminating in the recent experimental realization of so-called time crystals, has been made as discussed by the authors.
Abstract: Over the past decade, remarkable progress has occurred in the physics of closed quantum systems away from equilibrium, culminating in the recent experimental realization of so-called time crystals. This Progress Article surveys these developments.
239 citations
TL;DR: In this article, a theoretical analysis shows that many-body localization is compatible with physical systems that exhibit long-range interactions, thus opening manybody localization physics to a wide range of novel situations.
Abstract: Many-body localization is widely assumed to not be compatible with physical systems that exhibit long-range interactions. A new theoretical analysis shows that it is compatible with such systems, thus opening many-body localization physics to a wide range of novel situations.
100 citations
TL;DR: In this article, it was shown that MBL can arise in one-dimensional systems with 1/r interactions, a problem that exhibits charge confinement, and it can even arise in two dimensional systems with log r interactions.
Abstract: Many body localization (MBL) has emerged as a powerful paradigm for understanding non-equilibrium quantum dynamics Folklore based on perturbative arguments holds that MBL only arises in systems with short range interactions Here we advance non-perturbative arguments indicating that MBL can arise in systems with long range (Coulomb) interactions In particular, we show using bosonization that MBL can arise in one dimensional systems with ~ r interactions, a problem that exhibits charge confinement We also argue that (through the Anderson-Higgs mechanism) MBL can arise in two dimensional systems with log r interactions, and speculate that our arguments may even extend to three dimensional systems with 1/r interactions Our arguments are `asymptotic' (ie valid up to rare region corrections), yet they open the door to investigation of MBL physics in a wide array of long range interacting systems where such physics was previously believed not to arise
65 citations
TL;DR: Time crystals are states of matter that spontaneously break time translation symmetry as discussed by the authors, and they have been used to define Wigner symmetries and order parameters for many-body localized spin glass/Floquet time crystals.
Abstract: Time crystals are proposed states of matter that spontaneously break time translation symmetry. Despite much recent interest, there is no settled definition for such states and existing definitions only tangentially refer to the well-established foundations of spontaneous symmetry breaking. We offer a definition of time crystals, which treats time translation much like any other symmetry and follows the traditional recipe for defining Wigner symmetries and order parameters. Using our definition, we find: (i) systems with time independent Hamiltonians should not exhibit time translation symmetry breaking, and (ii) the many-body localized $\ensuremath{\pi}$ spin glass/Floquet time crystal can be viewed as breaking both a global internal symmetry and the time translation symmetry, as befits the two aspects of its name.
62 citations
TL;DR: In this article, the authors show via a variational approach and numerical exact diagonalization that tuning Haldane pseudopotentials in a model of interacting electrons in the lowest Landau level induces a quantum phase transition out of the isotropic Laughlin FQH liquid and into the fractional quantum Hall (FQH) nematic state.
Abstract: The fractional quantum Hall (FQH) nematic state is a conjectured state of matter in which FQH topological order coexists with spontaneously broken rotation symmetry. Recent experiments on GaAs quantum wells suggest this state, as well as the concomitant isotropic-nematic phase transition, may be realized in a two-dimensional electron gas at certain rational filling factors. Although effective field theories of the FQH nematic state have been constructed, there has been so far no explicit realization of this state as the ground state of a microscopic model of interacting electrons. The authors show via a variational approach and numerical exact diagonalization that tuning Haldane pseudopotentials in a model of interacting electrons in the lowest Landau level induces a quantum phase transition out of the isotropic Laughlin FQH liquid and into the FQH nematic state.
27 citations
TL;DR: It is shown that an analogous quantum clustering phenomenon takes place in the ground state subspace of a certain quantum optimization problem, which involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful.
Abstract: The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground state subspace of a certain quantum optimization problem. This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful. Quantum clusters correspond to macroscopically distinct subspaces of the full quantum ground state space which grow with the system size. We explicitly demonstrate that such clusters arise in the solution space of random quantum satisfiability (3-QSAT) at its satisfiability transition. We estimate both the number of these clusters and their internal entropy. The former are given by the number of hardcore dimer coverings of the core of the interaction graph, while the latter is related to the underconstrained degrees of freedom not touched by the dimers. We additionally provide new numerical evidence suggesting that the 3-QSAT satisfiability transition may coincide with the product satisfiability transition, which would imply the absence of an intermediate entangled satisfiable phase.
11 citations
TL;DR: Sondhi and Kivelson as mentioned in this paper argue that science prizes should better reflect how modern science is carried out, argue Shivaji Sondhi, and Steven Kivelsson.
Abstract: Science prizes should better reflect how modern science is carried out, argue Shivaji Sondhi and Steven Kivelson.
1 citations