Zero-temperature entanglement membranes in quantum circuits

Published

August 13, 2024

Author(s)

Grace Sommers, Sarang Gopalakrishnan, Michael Gullans, David Huse

Abstract

In chaotic quantum systems, the entanglement of a region A can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of A. Here, we interpret the tension of this "entanglement membrane" in terms of the rate at which information flows across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various space-time translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the circuits where this steady state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits, and is also present in some special non-stabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero- temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature.

Citation

Physical Review B

Volume

110

Issue

6

Pub Type

Journals

Download Paper

https://doi.org/10.1103/PhysRevB.110.064311

Local Download

Keywords

quantum entanglement, quantum many-body physics, statistical mechanics

Citation

Sommers, G. , Gopalakrishnan, S. , Gullans, M. and Huse, D. (2024), Zero-temperature entanglement membranes in quantum circuits, Physical Review B, [online], https://doi.org/10.1103/PhysRevB.110.064311, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=957715 (Accessed November 23, 2024)