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.

arXiv comment6+7 pages, 4+9 figures, added most updated version and SM

References in corpus (59)

• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• The large deviation approach to statistical mechanics
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Glassy dynamics of kinetically constrained models
• Classical simulation of quantum many-body systems with a tree tensor network
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Direct evaluation of large-deviation functions
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Nonequilibrium Markov processes conditioned on large deviations
• The computational complexity of PEPS
• Large deviations and ensembles of trajectories in stochastic models
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Operator space entanglement entropy in transverse Ising chain
• Algorithms for finite Projected Entangled Pair States
• Introduction to dynamical large deviations of Markov processes
• Universal cumulants of the current in diffusive systems on a ring
• Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
• A numerical approach to large deviations in continuous-time
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Exact Current Statistics of the ASEP with Open Boundaries
• Tensor Network Algorithms: a Route Map
• Ergodicity and large deviations in physical systems with stochastic dynamics
• Frenesy: time-symmetric dynamical activity in nonequilibria
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Unifying Projected Entangled Pair States contractions
• Cumulants and large deviations of the current through non-equilibrium steady states
• Population dynamics method with a multi-canonical feedback control
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Time Dependent Variational Principle for Tree Tensor Networks
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Rare behavior of growth processes via umbrella sampling of trajectories
• Conformal invariance in driven diffusive systems at high currents
• Importance sampling large deviations in nonequilibrium steady states. I
• Adaptive sampling of large deviations
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
• Direct sampling of projected entangled-pair states
• Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries
• Finite time large deviations via matrix product states
• Optimal sampling of dynamical large deviations via matrix product states
• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Approximate optimization, sampling and spin-glass droplets discovery with tensor networks
• Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
• Using tensor network states for multi-particle Brownian ratchets
• Computing time-periodic steady-state currents via the time evolution of tensor network states
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System

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