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Rare-event properties in a classical stochastic model describing the evolution of random unitary circuits
Physical Review E  (IF2.529),  Pub Date : 2021-09-16, DOI: 10.1103/physreve.104.034122
S. L. A. de Queiroz

We investigate the statistics of selected rare events in a $\left(1+1\right)$-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or annihilated at each step of the evolution process, according to rules which generally favor a growing cluster size. We apply a large-deviation approach based on biased Monte Carlo simulations, with suitable adaptations, to evaluate (a) the probability of ending up with a single particle at a specified final time ${t}_{f}$ and (b) the probability of having particles outside the light cone, defined by a “butterfly velocity” ${v}_{B}$, at ${t}_{f}$. Morphological features of single-particle final configurations are discussed, in connection with whether the location of such particle is inside or outside the light cone; we find that joint occurrence of both events of types (a) and (b) drives significant changes to such features, signaling a second-order phase transition.