Elusive phase transition in the replica limit of monitored systems
arXiv:2306.12166
Abstract
We study an exactly solvable model of monitored dynamics in a system of spin- particles with pairwise all-to-all noisy interactions, where each spin is continuously weakly measured along a random direction. Using the replica trick to incorporate the Born-rule weighting of measurement outcomes, we obtain an exact large- description of purification and of the statistics of local observables. We find that the nature of the phase transition strongly depends on the number of replicas: non-perturbative logarithmic corrections appear in the physically relevant limit and destroy the purifying phase present at finite integer . As a consequence, the purification time of an initially mixed state is always exponentially long in the system size, even at arbitrarily large measurement rate.
7+16 pages, 3+4 figures
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