Quantum Entanglement Growth under Random Unitary Dynamics
Characterizing how entanglement grows with time in a manybody 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 timedependent 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 KardarParisiZhang (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 RyuTakayanagi 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 leadingorder time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarsemore »
 Authors:

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 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics; Univ. of Oxford (United Kingdom). Theoretical Physics
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics
 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:
 Grant/Contract Number:
 SC0010526
 Type:
 Published Article
 Journal Name:
 Physical Review. X
 Additional Journal Information:
 Journal Volume: 7; Journal Issue: 3; Journal ID: ISSN 21603308
 Publisher:
 American Physical Society
 Research Org:
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22). Materials Sciences & Engineering Division; USDOE
 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; 1dimensional spin chains; chaotic systems; KardarParisiZhang equation; nonlinear dynamics
 OSTI Identifier:
 1372592
 Alternate Identifier(s):
 OSTI ID: 1424920
Nahum, Adam, Ruhman, Jonathan, Vijay, Sagar, and Haah, Jeongwan. Quantum Entanglement Growth under Random Unitary Dynamics. United States: N. p.,
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. 2017.
"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 manybody 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 timedependent 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 KardarParisiZhang (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 RyuTakayanagi 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 leadingorder 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.},
doi = {10.1103/PhysRevX.7.031016},
journal = {Physical Review. X},
number = 3,
volume = 7,
place = {United States},
year = {2017},
month = {7}
}