Coarse-grained dynamics of operator and state entanglement
By Cheryne Jonay, D. Huse, A. Nahum. 2018
177 citations recorded by the source corpus.
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 of the time evolution operator, and we discuss possible universality of $\mathcal{E}$ at low temperatures. Our theoretical ideas are tested against and informed by numerical results for a quantum-chaotic 1D spin Hamiltonian. These results are relevant to the broad class of chaotic many-particle systems or field theories with spatially local interactions, both in 1D and above.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/0c1d97364028c9a472e0095bce642c0096042f80
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Fracton phases of matter (2020, background): “[105] Cheryne Jonay, David A.”
- Localization in Fractonic Random Circuits (2018, background): “[71] Cheryne Jonay, David A Huse, and Adam Nahum, “Coarse-grained dynamics of operator and state entanglement,” arXiv preprint arXiv:1803.”
- Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, methodology): “It can also depend on the orientation of the membrane [50], but here we are interested only in membranes that are “horizontal” on large scales.”
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, background): “work which is a useful starting point for thinking about the scaling of entanglement in various situations ranging from holography [24, 42, 43] to unitary dynamics [6, 9, 13].”
- Random Quantum Circuits (2022, background): “2, though this is in general distinct from vE : we may argue via causality that E(vB) = vB and E (vB) = 1 (144).”
- Emergent statistical mechanics of entanglement in random unitary circuits (2018, background): “states that are not necessarily product states [25]:”
- Entanglement Membrane in Chaotic Many-Body Systems (2019, methodology): “[18] extracted the line tension associated with the von Neumann entropy for a chaotic Ising model directly from the operator entanglement of U(t).”