Journal Article

Quantum Entanglement Growth under Random Unitary Dynamics

Ruhman, Jonathan, Vijay, Sagar, Haah, Jeongwan, Nahum, Adam

2017

Overview

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.

• Publisher: American Physical Society
• Subject: 1-dimensional spin chains / chaotic systems / CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS / Condensed Matter Physics / CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY / Domain walls / Entanglement in field theory / entanglement production / Entropy / Evolution / Gates (circuits) / growth processes / Hamiltonian functions / Kardar-Parisi-Zhang equation / Membranes / Noise / nonequilibrium statistical mechanics / nonlinear dynamics / Quantum entanglement / Quantum Information / Quantum mechanics / quantum nonlocality / quantum simulation / quantum stochastic process / Quantum theory / Statistical mechanics / Statistical Physics / Stochastic models / Theoretical physics / Thermalization (energy absorption) / Time dependence / Tsunamis