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Entanglement Dynamics of Random GUE Hamiltonians

by Daniel Chernowitz, Vladimir Gritsev

Submission summary

As Contributors: Daniel Chernowitz
Arxiv Link: https://arxiv.org/abs/2001.00140v2
Date submitted: 2020-01-08
Submitted by: Chernowitz, Daniel
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Quantum Physics
Approach: Theoretical

Abstract

In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and SYK model. Along the way, we find general expressions for exponential n-point correlation functions in the gas of GUE eigenvalues.

Current status:
Editor-in-charge assigned


Submission & Refereeing History

Submission 2001.00140v2 on 8 January 2020

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