Dynamics of Fluctuations in Quantum Simple Exclusion Processes
Abstract
We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (QASEP) with periodic boundary conditions. The QASEP describes a chain of spinless fermions with random hoppings that are induced by a Markovian environment. We show that fluctuations of the fermionic degrees of freedom obey evolution equations of Lindblad type, and derive the corresponding Lindbladians. We identify the underlying algebraic structure by mapping them to nonHermitian spin chains and demonstrate that the operator space fragments into exponentially many (in system size) sectors that are invariant under time evolution. At the level of quadratic fluctuations we consider the Lindbladian on the sectors that determine the late time dynamics for the particular case of the quantum symmetric simple exclusion process (QSSEP). We show that the corresponding blocks in some cases correspond to known YangBaxter integrable models and investigate the levelspacing statistics in others. We carry out a detailed analysis of the steady states and slow modes that govern the late time behaviour and show that the dynamics of fluctuations of observables is described in terms of closed sets of coupled linear differentialdifference equations. The behaviour of the solutions to these equations is essentially diffusive but with relevant deviations, that at sufficiently late times and large distances can be described in terms of a continuum scaling limit which we construct. We numerically check the validity of this scaling limit over a significant range of time and space scales. These results are then applied to the study of operator spreading at large scales, focusing on outoftime ordered correlators and operator entanglement.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.02662
 Bibcode:
 2021arXiv210702662B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 67 pages, 12 figures