Quantum Entanglement Growth Under Random Unitary Dynamics
By A. Nahum, J. Ruhman, S. Vijay, Jeongwan Haah. 2016
768 citations recorded by the source corpus.
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium 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 $(\text{time})^{1/3}$ and are spatially correlated over a distance $\propto (\text{time})^{2/3}$. We derive KPZ universal behaviour 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 `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.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/835875b880f3770d3369d0dc42c08af0de5af965
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Citations in the corpus
- Many-Body Quantum Magic (2020, background): “[72] Adam Nahum, Jonathan Ruhman, Sagar Vijay, and”
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- Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, background): “Recent work by the authors and others [7, 25, 26] set to examine these questions in the context of local random unitary circuits, where a number of exact results can be derived for the average behavior of OTOCs and other relevant quantities.”
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