Entanglement entropy growth in stochastic conformal field theory and the KPZ class

Abstract

We introduce a model of effective conformal quantum field theory in dimension $d=1+1$ coupled to stochastic noise, where Kardar-Parisi-Zhang (KPZ) class fluctuations can be observed. The analysis of the quantum dynamics of the scaling operators reduces to the study of random trajectories in a random environment, modeled by Brownian vector fields. We use recent results on random walks in random environments to calculate the time-dependent entanglement entropy of a subsystem interval, starting from a factorized state. We find that the fluctuations of the entropy in the large deviation regime are governed by the universal Tracy-Widom distribution. This enlarges the KPZ class, previously observed in random circuit models, to a family of interacting many body quantum systems.

arXiv comment5 pages, plus references, plus Supp. Mat. (15 pages), 3 figures

References in corpus (25)

• Level-Spacing Distributions and the Airy Kernel
• Time-dependence of correlation functions following a quantum quench
• Shape Fluctuations and Random Matrices
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Emergent statistical mechanics of entanglement in random unitary circuits
• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• An exact solution for the KPZ equation with flat initial conditions
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• The one-dimensional KPZ equation and its universality class
• A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
• Flows, coalescence and noise
• Slow modes in passive advection
• Random-walk in Beta-distributed random environment
• Renormalization fixed point of the KPZ universality class
• Open Quantum Symmetric Simple Exclusion Process
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Entanglement production and information scrambling in a noisy spin system
• Diffusive Heat Waves in Random Conformal Field Theory
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Diffusion and signatures of localization in stochastic conformal field theory
• Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equation
• Sticky behavior of fluid particles in the compressible Kraichnan model
• Moderate deviations for diffusion in time dependent random media

Cited by in corpus (15)

• Inhomogeneous conformal field theory out of equilibrium
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Exact description of quantum stochastic models as quantum resistors
• Generic transport formula for a system driven by Markovian reservoirs
• The crossover from the Macroscopic Fluctuation Theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• KPZ physics and phase transition in a classical single random walker under continuous measurement
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Semi-classical theory of quantum stochastic resistors
• KPZ fluctuations in finite volume
• Driven Non-Unitary Dynamics of Quantum Critical Systems
• Domain-wall melting in all-to-all QSSEP from random-matrix theory