Zero-temperature entanglement membranes in quantum circuits
arxiv(2024)
摘要
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 cases where this dynamics is nonunitary and the 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.
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