Fractal, Logarithmic, and Volume-Law Entangled Nonthermal Steady States via Spacetime Duality

Ippoliti, Matteo; Rakovszky, Tibor; Khemani, Vedika

doi:10.1103/PhysRevX.12.011045

Title: Fractal, Logarithmic, and Volume-Law Entangled Nonthermal Steady States via Spacetime Duality

Journal Article · Wed Mar 09 00:00:00 EST 2022 · Physical Review. X

DOI:https://doi.org/10.1103/PhysRevX.12.011045· OSTI ID:1854062

; Rakovszky, Tibor; Khemani, Vedika

The extension of many-body quantum dynamics to the nonunitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time, on one hand, and unitarity and nonunitarity, on the other, can be used to realize steady-state phases of nonunitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size—from logarithmic to extensive to fractal. We show how these outcomes in nonunitary circuits (that are “spacetime dual” to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets “radiated away” from one edge of the system. In spacetime duals of chaotic unitary circuits, this mapping allows us to analytically derive a nonthermal volume-law entangled phase with a universal logarithmic correction to the entropy, previously observed in unitary-measurement dynamics. Notably, we also find robust steady-state phases with fractal entanglement scaling, S(ℓ)~ℓ^α with tunable 0 < α < 1 for subsystems of size ℓ in one dimension. We present an experimental protocol for preparing these novel steady states with only a vanishing density of postselected measurements via a type of “teleportation” between spacelike and timelike slices of quantum circuits.

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Research Organization:: Stanford Univ., CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Defense Advanced Research Projects Agency (DARPA); Sloan Foundation; Gordon and Betty Moore Foundation; Stanford Q-Farm Bloch Postdoctoral Fellowship

Grant/Contract Number:: SC0021111; GBMF8686

OSTI ID:: 1854062

Alternate ID(s):: OSTI ID: 1980360

Journal Information:: Physical Review. X, Journal Name: Physical Review. X Vol. 12 Journal Issue: 1; ISSN 2160-3308

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Fractal, Logarithmic, and Volume-Law Entangled Nonthermal Steady States via Spacetime Duality

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