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Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process

by Denis Bernard, Ludwig Hruza

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Submission summary

Authors (as registered SciPost users): Ludwig Hruza
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-09-29
Date submitted: 2023-09-16 14:02
Submitted by: Hruza, Ludwig
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Mathematical Physics
  • Quantum Physics
  • Statistical and Soft Matter Physics
Approach: Theoretical


Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We confirm this observation by studying a suitable toy model for mesoscopic transport~: the open quantum symmetric simple exclusion process (QSSEP). We derive exact formulae for its mutual information between different subsystems in the steady state and show that it satisfies a volume law. Surprisingly, the QSSEP entanglement properties only depend on data related to its transport properties and we suspect that such a relation might hold for more general mesoscopic systems. Exploiting the free probability structure of QSSEP, we obtain these results by developing a new method to determine the eigenvalue spectrum of sub-blocks of random matrices from their so-called local free cumulants -- a mathematical result on its own with potential applications in the theory of random matrices. As an illustration of this method, we show how to compute expectation values of observables in systems satisfying the Eigenstate Thermalization Hypothesis (ETH) from the local free cumulants.

Author comments upon resubmission

Thanks for the minor comments from the referees. We implemented them all, see below.

List of changes

- abstract, 3rd sentence: added "in the steady state"
- Introduction, 3rd paragraph, 2nd sentence: added "adjacent" and replaced "thermal"->"Gibbs"
- Last sentence on p. 3: added "In this article we are only interested in the steady state distribution of coherences, which is unique regardless of the initial condition."
- Last sentence on p. 4: modified "This also shows that in the equilibrium case where na = nb, all eigenvalues are equal to na. That is, dσ[c1,c2](λ) = δ(λ−na)dλ is independent of the interval [c1, c2]"

Published as SciPost Phys. 15, 175 (2023)

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