The Experts below are selected from a list of 33303 Experts worldwide ranked by ideXlab platform
Marcos Rigol - One of the best experts on this subject based on the ideXlab platform.
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Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians.
Physical review letters, 2020Co-Authors: Patrycja Łydżba, Marcos Rigol, Lev VidmarAbstract:The Eigenstate entanglement entropy is a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, the average Eigenstate entanglement entropy (over all Hamiltonian Eigenstates) has a volume-law coefficient that generally depends on the subsystem fraction. In contrast, it is maximal (subsystem fraction independent) in quantum-chaotic models. Using random matrix theory for quadratic Hamiltonians, we obtain a closed-form expression for the average Eigenstate entanglement entropy as a function of the subsystem fraction. We test it against numerical results for the quadratic Sachdev-Ye-Kitaev model and show that it describes the results for the power-law random banded matrix model (in the delocalized regime). We show that localization in quasimomentum space produces (small) deviations from our analytic predictions.
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Eigenstate Thermalization in a Locally Perturbed Integrable System.
Physical review letters, 2020Co-Authors: Marlon Brenes, Tyler Leblond, John Goold, Marcos RigolAbstract:Eigenstate thermalization is widely accepted as the mechanism behind thermalization in generic isolated quantum systems. Using the example of a single magnetic defect embedded in the integrable spin-1/2 XXZ chain, we show that locally perturbing an integrable system can give rise to Eigenstate thermalization. Unique to such setups is the fact that thermodynamic and transport properties of the unperturbed integrable chain emerge in properties of the Eigenstates of the perturbed (nonintegrable) one. Specifically, we show that the diagonal matrix elements of observables in the perturbed Eigenstates follow the microcanonical predictions for the integrable model, and that the ballistic character of spin transport in the integrable model is manifest in the behavior of the off-diagonal matrix elements of the current operator in the perturbed Eigenstates.
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Eigenstate thermalization in the two dimensional transverse field ising model ii off diagonal matrix elements of observables
Physical Review E, 2017Co-Authors: Rubem Mondaini, Marcos RigolAbstract:: We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the Eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the structure of the matrix elements. In particular, we show that a general result of the theory of random matrices, namely, the value 2 of the ratio of variances (diagonal to off-diagonal) of the matrix elements of Hermitian operators, occurs in the quantum chaotic regime. Furthermore, we explore the behavior of the off-diagonal matrix elements of observables as a function of the Eigenstate energy differences and show that it is in accordance with the Eigenstate thermalization hypothesis ansatz.
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Eigenstate thermalization in the two dimensional transverse field ising model
Physical Review E, 2016Co-Authors: Rubem Mondaini, Keith R. Fratus, Mark Srednicki, Marcos RigolAbstract:We study the onset of Eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two nonequivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the Eigenstates of the Hamiltonian. An analysis of finite size effects reveals that quantum chaos and Eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.
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emergent Eigenstate solution to quantum dynamics far from equilibrium
arXiv: Statistical Mechanics, 2015Co-Authors: Lev Vidmar, Deepak Iyer, Marcos RigolAbstract:The quantum dynamics of interacting many-body systems has become a unique venue for the realization of novel states of matter. Here we unveil a new class of nonequilibrium states that are Eigenstates of an emergent local Hamiltonian. The latter is explicitly time dependent and, even though it does not commute with the physical Hamiltonian, it behaves as a conserved quantity of the time-evolving system. We discuss two examples in which the emergent Eigenstate solution can be applied for an extensive (in system size) time: transport in one-dimensional lattices with initial particle (or spin) imbalance, and sudden expansion of quantum gases in optical lattices. We focus on noninteracting spinless fermions, hard-core bosons, and the Heisenberg model. We show that current-carrying states can be ground states of emergent local Hamiltonians, and that they can exhibit a quasimomentum distribution function that is peaked at nonzero (and tunable) quasimomentum. We also show that time-evolving states can be highly-excited Eigenstates of emergent local Hamiltonians, with an entanglement entropy that does not exhibit volume-law scaling.
Yichen Huang - One of the best experts on this subject based on the ideXlab platform.
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Eigenstate entanglement in the sachdev ye kitaev model
Physical Review D, 2019Co-Authors: Yichen HuangAbstract:We study the entanglement entropy of Eigenstates (including the ground state) of the Sachdev-Ye-Kitaev model. We argue for a volume law, whose coefficient can be calculated analytically from the density of states. The coefficient depends on not only the energy density of the Eigenstate but also the subsystem size. Very recent numerical results of Liu et al. confirm our analytical results.
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Universal Eigenstate entanglement of chaotic local Hamiltonians
Nuclear Physics B, 2019Co-Authors: Yichen HuangAbstract:Abstract In systems governed by “chaotic” local Hamiltonians, we conjecture the universality of Eigenstate entanglement (defined as the average entanglement entropy of all Eigenstates) by proposing an exact formula for its dependence on the subsystem size. This formula is derived from an analytical argument based on a plausible assumption, and is supported by numerical simulations.
Manuel Vielma - One of the best experts on this subject based on the ideXlab platform.
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Eigenstate thermalization in the Sachdev-Ye-Kitaev model
Journal of High Energy Physics, 2017Co-Authors: Julian Sonner, Manuel VielmaAbstract:The Eigenstate thermalization hypothesis (ETH) explains how closed unitary quantum systems can exhibit thermal behavior in pure states. In this work we examine a recently proposed microscopic model of a black hole in AdS 2 , the so-called Sachdev-Ye-Kitaev (SYK) model. We show that this model satisfies the Eigenstate thermalization hypothesis by solving the system in exact diagonalization. Using these results we also study the behavior, in Eigenstates, of various measures of thermalization and scrambling of information. We establish that two-point functions in finite-energy Eigenstates approximate closely their thermal counterparts and that information is scrambled in individual Eigenstates. We study both the Eigenstates of a single random realization of the model, as well as the model obtained after averaging of the random disordered couplings. We use our results to comment on the implications for thermal states of a putative dual theory, i.e. the AdS 2 black hole.
Antonello Scardicchio - One of the best experts on this subject based on the ideXlab platform.
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clustering of nonergodic Eigenstates in quantum spin glasses
Physical Review Letters, 2017Co-Authors: C. L. Baldwin, C R Laumann, Antonello ScardicchioAbstract:: The two primary categories for Eigenstate phases of matter at a finite temperature are many-body localization (MBL) and the Eigenstate thermalization hypothesis (ETH). We show that, in the paradigmatic quantum p-spin models of the spin-glass theory, Eigenstates violate the ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the nonergodic phase at a small transverse field from an ergodic phase at a large transverse field. The nonergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in the spin-glass theory. We show that the nonergodic Eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an Eigenstate variant of the Edwards-Anderson order parameter.
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Many-body localization beyond Eigenstates in all dimensions
Physical Review B, 2016Co-Authors: Anushya Chandran, C R Laumann, Arijeet Pal, Antonello ScardicchioAbstract:Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual Eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the Eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators (l$^*$-bits) underlie localization in such systems. In dimensions $d>1$, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to l$^*$-bits. Physical consequences of l$^*$-bits include the possibility of an Eigenstate phase transition within the MBL phase unrelated to the dynamical transition in $d=1$ and thermal Eigenstates at all parameters in $d>1$. Near-term experiments in ultra-cold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of l$^*$-bits.Comment: 12 pages, 5 figure
Keith R. Fratus - One of the best experts on this subject based on the ideXlab platform.
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Spontaneous Symmetry Breaking and Eigenstate Thermalization
2017Co-Authors: Keith R. FratusAbstract:Author(s): Fratus, Keith Richard | Advisor(s): Srednicki, Mark | Abstract: Over the last several decades, two theoretical tools have been indispensable in the field of statistical physics. Spontaneous symmetry breaking has allowed for the description of systems which exhibit second order phase transitions, while the Eigenstate thermalization hypothesis has provided a theoretical framework for understanding how isolated quantum many-body systems come to thermal equilibrium. In this dissertation, we will explore the compatibility of these two paradigms of theoretical physics.We will begin with a brief introduction to the relevant topics discussed in the main body of the dissertation, along with a brief overview of the numerical tools used in the subsequent investigations.Following this, we will numerically explore the compatibility between spontaneous symmetry breaking and Eigenstate thermalization through a sequence of papers which have been previously published by myself and a collection of other authors. We will study the compatibility of these two theoretical frameworks through an exact diagonalization and Quantum Monte Carlo study of the Transverse-Field Ising model, a quantum non-integrable system which, we argue, displays both spontaneous symmetry breaking and Eigenstate thermalization.Following this exposition, we will briefly comment on several corollaries which follow from these previously published papers, some of which we are currently preparing to incorporate into future publications. These corollaries largely focus on the subject of time evolution in quantum systems which display both spontaneous symmetry breaking and Eigenstate thermalization, as well as the possibility that individual Eigenstates of such systems may contain information about the critical behaviour of the corresponding finite-temperature phase transition.
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Eigenstate thermalization in the two dimensional transverse field ising model
Physical Review E, 2016Co-Authors: Rubem Mondaini, Keith R. Fratus, Mark Srednicki, Marcos RigolAbstract:We study the onset of Eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two nonequivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the Eigenstates of the Hamiltonian. An analysis of finite size effects reveals that quantum chaos and Eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.
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Eigenstate thermalization in systems with spontaneously broken symmetry
Physical Review E, 2015Co-Authors: Keith R. Fratus, Mark SrednickiAbstract:A strongly nonintegrable system is expected to satisfy the Eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy Eigenstate is the same as the thermal value. This must be revised if the observable is an order parameter for a spontaneously broken symmetry, which has multiple thermal values. We propose that in this case the system is unstable towards forming nearby Eigenstates which yield each of the allowed thermal values. We provide strong evidence for this from a numerical study of the two-dimensional transverse-field quantum Ising model.
