Elusive phase transition in the replica limit of monitored systems
We study an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is constantly perturbed by weak measurements of the spin component in a random direction. We make use of the replica trick to account for the...
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Zusammenfassung: | We study an exactly solvable model of monitored dynamics in a system of $N$
spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each
spin is constantly perturbed by weak measurements of the spin component in a
random direction. We make use of the replica trick to account for the Born's
rule weighting of the measurement outcomes in the study of purification and
other observables, with an exact description in the large-$N$ limit. We find
that the nature of the phase transition strongly depends on the number $n$ of
replicas used in the calculation, with the appearance of non-perturbative
logarithmic corrections that destroy the disentangled/purifying phase in the
relevant $n \rightarrow 1$ replica limit. Specifically, we observe that the
purification time of a mixed state in the weak measurement phase is always
exponentially long in the system size for arbitrary strong measurement rates. |
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DOI: | 10.48550/arxiv.2306.12166 |