Kavli Affiliate: Matthew P. A. Fisher
| First 5 Authors: Yaodong Li, Sagar Vijay, Matthew P. A. Fisher, ,
| Summary:
Monitored quantum dynamics reveal quantum state trajectories which exhibit a
rich phenomenology of entanglement structures, including a transition from a
weakly-monitored volume law entangled phase to a strongly-monitored area law
phase. For one-dimensional hybrid circuits with both random unitary dynamics
and interspersed measurements, we combine analytic mappings to an effective
statistical mechanics model with extensive numerical simulations on hybrid
Clifford circuits to demonstrate that the universal entanglement properties of
the volume law phase can be quantitatively described by a fluctuating
entanglement domain wall that is equivalent to a "directed polymer in a random
environment" (DPRE). This relationship improves upon a qualitative "mean-field"
statistical mechanics of the volume-law-entangled phase [1, 2]. For the
Clifford circuit in various geometries, we obtain agreement between the
subleading entanglement entropies and error correcting properties of the
volume-law phase (which quantify its stability to projective measurements) with
predictions of the DPRE. We further demonstrate that depolarizing noise in the
hybrid dynamics near the final circuit time can drive a continuous phase
transition to a non-error correcting volume law phase that is not immune to the
disentangling action of projective measurements. We observe this transition in
hybrid Clifford dynamics, and obtain quantitative agreement with critical
exponents for a "pinning" phase transition of the DPRE in the presence of an
attractive interface.
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