Optimal sampling of dynamical large deviations in two dimensions via tensor networks

Abstract

We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open boundaries, in lattices of up to 40x40 sites. We show that at long-times both models have phase transitions between active and inactive dynamical phases. For the 2D East model we find that this trajectory transition is of the first-order, while for the SSEP we find indications of a second order transition. We then show how the PEPS can be used to implement a trajectory sampling scheme capable of directly accessing rare trajectories. We also discuss how the methods described here can be extended to study rare events at finite times.

6+7 pages, 4+9 figures, added most updated version and SM

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Cited by in corpus (10)

• Classically estimating observables of noiseless quantum circuits
• Confined run and tumble particles with non-Markovian tumbling statistics
• Stochastic thermodynamic bounds on logical circuit operation
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Finding the effective dynamics to make rare events typical in chaotic maps
• Optimal finite-differences discretization for the diffusion equation from the perspective of large-deviation theory
• Rejection-free quantum Monte Carlo in continuous time from transition path sampling
• Chemical master equation parameter exploration using DMRG
• Sampling two-dimensional isometric tensor network states
• Self-interacting processes via Doob conditioning