Using matrix product states to study the dynamical large deviations of kinetically constrained models

Abstract

Here we demonstrate that tensor network techniques - originally devised for the analysis of quantum many-body problems - are well suited for the detailed study of rare event statistics in kinetically constrained models (KCMs). As concrete examples we consider the Fredrickson-Andersen and East models, two paradigmatic KCMs relevant to the modelling of glasses. We show how variational matrix product states allow to numerically approximate - systematically and with high accuracy - the leading eigenstates of the tilted dynamical generators which encode the large deviation statistics of the dynamics. Via this approach we can study system sizes beyond what is possible with other methods, allowing us to characterise in detail the finite size scaling of the trajectory-space phase transition of these models, the behaviour of spectral gaps, and the spatial structure and "entanglement" properties of dynamical phases. We discuss the broader implications of our results.

15 pages (including supplemental material), 3+18 figures. Extended Supplemental material

References in corpus (32)

• The density-matrix renormalization group in the age of matrix product states
• Theoretical perspective on the glass transition and amorphous materials
• 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
• DMRG and periodic boundary conditions: a quantum information perspective
• From density-matrix renormalization group to matrix product states
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Entropy scaling and simulability by Matrix Product States
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Fluctuations and response of nonequilibrium states
• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Strongly correlated growth of Rydberg aggregates in a vapor cell
• A numerical approach to large deviations in continuous-time
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Quantum mechanical and information theoretic view on classical glass transitions
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Locality and digital quantum simulation of power-law interactions
• DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
• Quantum chaos dynamics in long-range power law interaction systems
• Entanglement production and information scrambling in a noisy spin system
• Noisy Coupled Qubits: Operator Spreading and the Fredrickson-Andersen Model
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Exact matrix product decay modes of a boundary driven cellular automaton
• Unfolding Tagged Particle Histories in Single-File Diffusion: Exact Single- and Two-Tag Local Times Beyond Large Deviation Theory
• Two extensions of exact non-equilibrium steady states of a boundary driven cellular automaton
• Rare event simulation for stochastic dynamics in continuous time

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• Slow dynamics and large deviations in classical stochastic Fredkin chains
• A large deviation theory perspective on nanoscale transport phenomena
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically-constrained East Model
• A Deep Learning Functional Estimator of Optimal Dynamics for Sampling Large Deviations
• Using tensor network states for multi-particle Brownian ratchets
• Computing time-periodic steady-state currents via the time evolution of tensor network states
• Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Dynamical phase coexistence in the Fredrickson-Andersen model
• Matrix Product Belief Propagation for reweighted stochastic dynamics over graphs
• Finding the effective dynamics to make rare events typical in chaotic maps
• Stochastic thermodynamic bounds on logical circuit operation
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Quantum turnstiles for robust measurement of full counting statistics
• Entropy Governed by the Absorbing State of Directed Percolation
• Adaptive power method for estimating large deviations in Markov chains
• Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control
• Emergent information dynamics in many-body interconnected systems
• Exact results on the dynamics of the stochastic Floquet-East model
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
• Stretched exponential to power-law: crossover of relaxation in a kinetically constrained model
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory
• Self-interacting processes via Doob conditioning
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems
• Making rare events typical in $d$-dimensional chaotic maps
• Restoring detailed balance in non-Hermitian Markov processes
• Mechanical analysis of a dynamical phase transition for particles in a channel