Entanglement features of random Hamiltonian dynamics

You, Yi-Zhuang; Gu, Yingfei

doi:10.1103/physrevb.98.014309

Cited by 44 publications

(53 citation statements)

References 95 publications

(131 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the powerset of {R 1 , R 2 , ..., R S }. A similar relation has recently been studied in the context of random dynamics in [17]. A representation of a typical term in the sum is shown in Figure 2b.…”

Section: Thermalization Of Completely Random Product Statessupporting

confidence: 64%

“…The OTOCs in (17) are to be computed for operators in the past that do not move states out of H M (and act by zero on states outside); in the examples following (15),Õ R will conserve local energy density or subsystem charge, respectively. We also clearly have [π M ,Õ R ] = 0, so according to (15) the mutual information bounds the effect of these operators in the most intuitive way.…”

Section: Finite Temperature Extensionmentioning

confidence: 99%

See 1 more Smart Citation

Chaos and high temperature pure state thermalization

Lensky

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

Classical arguments for thermalization of isolated systems do not apply in a straightforward way to the quantum case. Recently, there has been interest in diagnostics of quantum chaos in manybody systems. In the classical case, chaos is a popular explanation for the legitimacy of the methods of statistical physics. In this work, we relate a previously proposed criteria of quantum chaos in the unitary time evolution operator to the entanglement entropy growth for a far-from-equilibrium initial pure state. By mapping the unitary time evolution operator to a doubled state, chaos can be characterized by suppression of mutual information between subsystems of the past and that of the future. We show that when this mutual information is small, a typical unentangled initial state will evolve to a highly entangled final state. Our result provides a more concrete connection between quantum chaos and thermalization in many-body systems. * ydl@stanford.edu 1 arXiv:1805.03675v2 [cond-mat.stat-mech]

show abstract

Section: Thermalization Of Completely Random Product Statessupporting

confidence: 64%

Section: Finite Temperature Extensionmentioning

confidence: 99%

Chaos and high temperature pure state thermalization

Lensky

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…This notion of quantum Lyapunov exponent has since received intense scrutiny; it is related to information scrambling [4,6,7,8] and thermalization [9,10,11,12], it can be measured experimentally [13,14,15,16,17,18,19,20,21,22,23], it relates to operator growth [24,25,26,27,28,29,30,31], and can be computed either numerically or analytically in many model systems [5,24,25,26,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,…”

Section: Introductionmentioning

confidence: 99%

Quantum Lyapunov spectrum

Gharibyan

Hanada

Swingle

et al. 2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a manybody localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems.

show abstract

“…Quantum Lyapunov exponents have by now received intense scrutiny. They can be measured experimentally [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22], are related to operator growth [23] [24] [25] [26] [27] [28] [29] [30], and can be computed either numerically or analytically in many model systems [ [50]. Figure 1: 1a represents the time ordered correlation function on the two fold contour and 1b represents the OTOC.…”

Section: Introductionmentioning

confidence: 99%

Thermalization and chaos in QED3

Steinberg

Swingle

2019

Phys. Rev. D

View full text Add to dashboard Cite

We study the real time dynamics of N F flavors of fermions coupled to a U (1) gauge field in 2 + 1 dimensions to leading order in a 1/N F expansion. For large enough N F , this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in 1/N F . We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance. t ß t ß t ß (a) t ß t ß t ß (b)

show abstract

Entanglement features of random Hamiltonian dynamics

Cited by 44 publications

References 95 publications

Chaos and high temperature pure state thermalization

Chaos and high temperature pure state thermalization

Quantum Lyapunov spectrum

Thermalization and chaos in QED3

Contact Info

Product

Resources

About