Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System

Kim, HyungWon; Huse, David A.

doi:10.1103/physrevlett.111.127205

Cited by 494 publications

(534 citation statements)

References 24 publications

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“…V. Here, we consider the simplest case, the saturation of the entanglement entropy Sðx; tÞ across a single cut (or for a single interval). We reproduce a simple scaling function known from other contexts [8,10,21].…”

Section: A Scaling Form For Entanglement Saturationmentioning

confidence: 99%

“…The linearity of the leading t dependence is expected from rigorous bounds for various 1 þ 1D random circuits [39][40][41]. Linear growth is also generic for quenches in translationally invariant 1D systems [3,21]. The fluctuations grow as wðx; tÞ ≡ ⟪Sðx;…”

Section: Surface Growth In 1dmentioning

confidence: 99%

“…This irreversible growth of entanglementquantified by the growth of the von Neumman entropyis important for several reasons. It is an essential part of thermalization, and as a result has been addressed in diverse contexts ranging from conformal field theory [1][2][3][4] and holography [5][6][7][8][9][10][11][12] to integrable [13][14][15][16][17][18][19], nonintegrable [20][21][22][23], and strongly disordered spin chains [24][25][26][27][28][29][30]. Entanglement growth is also of practical importance as the crucial obstacle to simulating quantum dynamics numerically, for example, using matrix product states or the density matrix renormalization group [31].…”

Section: Introductionmentioning

confidence: 99%

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Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated KardarParisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like ðtimeÞ 1=3 and are spatially correlated over a distance ∝ ðtimeÞ 2=3 . We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the wellstudied problem of pinning of a membrane or domain wall by disorder.

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Section: A Scaling Form For Entanglement Saturationmentioning

confidence: 99%

Section: Surface Growth In 1dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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“…In contrast, the eigenstates of MBL systems can be obtained from product states by quasilocal unitary transformations and have low entanglement that obeys the "area law" [9,14]. Furthermore, ergodic and MBL phases are distinguished by the dynamics of entanglement following a quantum quench from initially nonentangled states: In the former case, entanglement spreads ballistically and grows linearly in time [15,16], while in the latter case, the spreading is logarithmic in time [17][18][19]. The latter property has been understood from the phenomenological theory of the MBL phase based on the LIOMs [9,10].…”

Section: Introductionmentioning

confidence: 99%

Criterion for Many-Body Localization-Delocalization Phase Transition

2015

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We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum manybody systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's eigenstates, finding a qualitatively different behavior in the manybody localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter GðLÞ ¼ hlnðV nm =δÞi, which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter GðLÞ decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when GðLÞ is independent of system size, GðLÞ ¼ G c ∼ 1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1=2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions.

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“…However, since the Gutzwiller ansatz wavefunction is a product state, it has zero entanglement entropy for any partitioning of the system. GMFT is therefore capable of capturing BG dynamics but it cannot capture thermalization and MBL phases [57], which after taken out of equilibrium, e.g., using a quantum quench, exhibit a linear [58] and logarithmic [59] growth of the entanglement entropy, respectively, with time.…”

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confidence: 99%

Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder

et al. 2017

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Motivated by recent optical lattice experiments [J.-y. Choi et al., Science 352, 1547], we study the dynamics of strongly interacting bosons in the presence of disorder in two dimensions. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system.

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Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System

Cited by 494 publications

References 24 publications

Quantum Entanglement Growth under Random Unitary Dynamics

Quantum Entanglement Growth under Random Unitary Dynamics

Criterion for Many-Body Localization-Delocalization Phase Transition

Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder

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