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Title: Quantum Entanglement Growth under Random Unitary Dynamics

Abstract

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 Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time) 1/3 and are spatially correlated over a distance ∝(time) 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 coarsemore » 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 well-studied problem of pinning of a membrane or domain wall by disorder.« less

Authors:
 [1];  [2];  [3];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics; Univ. of Oxford (United Kingdom). Theoretical Physics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics; Univ. of California, Santa Barbara, CA (United States). Kavli Institute for Theoretical Physics
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1372592
Alternate Identifier(s):
OSTI ID: 1424920
Grant/Contract Number:  
SC0010526
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Volume: 7; Journal Issue: 3; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Condensed Matter Physics; Quantum Information; Statistical Physics; Entanglement in field theory; entanglement production; growth processes; nonequilibrium statistical mechanics; quantum entanglement; quantum nonlocality; quantum simulation; quantum stochastic process; 1-dimensional spin chains; chaotic systems; Kardar-Parisi-Zhang equation; nonlinear dynamics

Citation Formats

Nahum, Adam, Ruhman, Jonathan, Vijay, Sagar, and Haah, Jeongwan. Quantum Entanglement Growth under Random Unitary Dynamics. United States: N. p., 2017. Web. doi:10.1103/PhysRevX.7.031016.
Nahum, Adam, Ruhman, Jonathan, Vijay, Sagar, & Haah, Jeongwan. Quantum Entanglement Growth under Random Unitary Dynamics. United States. doi:10.1103/PhysRevX.7.031016.
Nahum, Adam, Ruhman, Jonathan, Vijay, Sagar, and Haah, Jeongwan. Mon . "Quantum Entanglement Growth under Random Unitary Dynamics". United States. doi:10.1103/PhysRevX.7.031016.
@article{osti_1372592,
title = {Quantum Entanglement Growth under Random Unitary Dynamics},
author = {Nahum, Adam and Ruhman, Jonathan and Vijay, Sagar and Haah, Jeongwan},
abstractNote = {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 Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time)1/3 and are spatially correlated over a distance ∝(time)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 well-studied problem of pinning of a membrane or domain wall by disorder.},
doi = {10.1103/PhysRevX.7.031016},
journal = {Physical Review. X},
number = 3,
volume = 7,
place = {United States},
year = {2017},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
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DOI: 10.1103/PhysRevX.7.031016

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