SciPost Physics

SciPost Phys. 12, 042 (2022) · published 28 January 2022

• doi: 10.21468/SciPostPhys.12.1.042
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. The Q-ASEP 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 non-Hermitian 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 (Q-SSEP). We show that the corresponding blocks in some cases correspond to known Yang-Baxter integrable models and investigate the level-spacing 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 differential-difference 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 out-of-time ordered correlators and operator entanglement.

• Martinez-Azcona et al., Stochastic Operator Variance: An Observable to Diagnose Noise and Scrambling
  Phys. Rev. Lett. 131, 160202 (2023) [Crossref]
• Christopoulos et al., Universal Out-of-Equilibrium Dynamics of 1D Critical Quantum Systems Perturbed by Noise Coupled to Energy
  Phys. Rev. X 13, 011043 (2023) [Crossref]
• McCulloch et al., Full Counting Statistics of Charge in Chaotic Many-Body Quantum Systems
  Phys. Rev. Lett. 131, 210402 (2023) [Crossref]
• Doyon et al., Ballistic macroscopic fluctuation theory
  SciPost Phys. 15, 136 (2023) [Crossref]
• Langlett et al., Noise-induced universal diffusive transport in fermionic chains
  Phys. Rev. B 108, L180303 (2023) [Crossref]
• Poboiko et al., Theory of Free Fermions under Random Projective Measurements
  Phys. Rev. X 13, 041046 (2023) [Crossref]
• Turkeshi et al., Enhanced entanglement negativity in boundary-driven monitored fermionic chains
  Phys. Rev. B 106, 024304 (2022) [Crossref]
• Hruza et al., Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP, and Free Probability
  Phys. Rev. X 13, 011045 (2023) [Crossref]
• Murciano et al., Symmetry-resolved Page curves
  Phys. Rev. D 106, 046015 (2022) [Crossref]
• Tiutiakina et al., Frame potential of Brownian SYK model of Majorana and Dirac fermions
  J. High Energ. Phys. 2024, 115 (2024) [Crossref]