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Coarse-grained Dynamics of Operator and State Entanglement by Jonay, Cheryne; Huse, David A.; Nahum, Adam is a scholarly article available to read on EtoBox.

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We give a detailed theory for the leading coarse-grained dynamics of entanglement entropy of states and of operators in generic short-range interacting quantum many-body systems. This includes operators spreading under Heisenberg time evolution, which we find are much less entangled than "typical" operators of the same spatial support. Extending previous conjectures based on random circuit dynamics, we provide evidence that the leading-order entanglement dynamics of a given chaotic system are determined by a function $\mathcal{E}(v)$, which is model-dependent, but which we argue satisfies certain general constraints. In a minimal membrane picture, $\mathcal{E}(v)$ is the "surface tension" of the membrane and is a function of the membrane's orientation $v$ in spacetime. For one-dimensional (1D) systems this surface tension is related by a Legendre transformation to an entanglement entropy growth rate $\Gamma(\partial S/\partial x)$ which depends on the spatial "gradient" of the entanglement entropy $S(x,t)$ across the cut at position $x$. We show how to extract the entanglement growth functions numerically in 1D at infinite temperature using the concept of the operator entanglement

Author

Jonay, Cheryne; Huse, David A.; Nahum, Adam

Published

2018

Language

EN