Many-body localization in the Heisenberg<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math>magnet in a random field

Žnidarič, Marko; Prosen, Tomaž; Prelovšek, P.

doi:10.1103/physrevb.77.064426

Cited by 963 publications

(1,051 citation statements)

References 34 publications

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“…However, we do expect saturation to remain discontinuous, as in 1D [Eq. (24)], occurring via a transition between an optimal membrane configuration that reaches the bottom of the space-time slice and one (with E ¼ πR 2 ) that does not.…”

Section: Sðtþ∼mentioning

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: Sðtþ∼mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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“…The MBL phase resembles noninteracting Anderson insulators in some ways (e.g., spatial correlations decay exponentially, and eigenstates have area-law entanglement [35]). However, there are also important distinctions in entanglement dynamics [36,37], dephasing [38][39][40], linear [41] and nonlinear [42][43][44][45][46][47][48] response, and the entanglement spectrum [49,50]. These developments (reviewed in Refs.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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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.

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“…For the remainder of this Section we turn to the commonly studied random field Heisenberg chain 16,64 numerical simulations we diagonalize the Hamiltonian exactly, with n = 8 spins. In all cases we average over 1000 repetitions.…”

Section: B Intrinsic Bath Size Vs Disordermentioning

confidence: 99%

“…One prominent result is the (LiebRobinson) linear in-time growth of entanglement in ballistic and diffusive systems 12 . By contrast, there exist localized interacting many-body systems, known as "manybody localized" phases [13][14][15][16][17][18][19][20][21][22] , whose subsystems' entanglement grows only logarithmically in time 16,[23][24][25][26] .…”

Section: Introductionmentioning

confidence: 99%

Multipoint entanglement in disordered systems

2017

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We develop an approach to characterize excited states of disordered many-body systems using spatially resolved structures of entanglement. We show that the behavior of the mutual information (MI) between two parties of a many-body system can signal a qualitative difference between thermal and localized phases -MI is finite in insulators while it approaches zero in the thermodynamic limit in the ergodic phase. Related quantities, such as the recently introduced Codification Volume (CV), are shown to be suitable to quantify the correlation length of the system. These ideas are illustrated using prototypical non-interacting wavefunctions of localized and extended particles and then applied to characterize states of strongly excited interacting spin chains. We especially focus on evolution of spatial structure of quantum information between high temperature diffusive and many-body localized phases believed to exist in these models. We study MI as a function of disorder strength both averaged over the eigenstates and in time-evolved product states drawn from continuously deformed family of initial states realizable experimentally. As expected, spectral and time-evolved averages coincide inside the ergodic phase and differ significantly outside. We also highlight dispersion among the initial states within the localized phase -some of these show considerable generation and delocalization of quantum information.

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Many-body localization in the HeisenbergXXZmagnet in a random field

Cited by 963 publications

References 34 publications

Quantum Entanglement Growth under Random Unitary Dynamics

Quantum Entanglement Growth under Random Unitary Dynamics

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

Multipoint entanglement in disordered systems

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