# Entanglement Dynamics of Random GUE Hamiltonians

### Submission summary

 As Contributors: Daniel Chernowitz Arxiv Link: https://arxiv.org/abs/2001.00140v3 (pdf) Date accepted: 2021-03-15 Date submitted: 2021-02-23 12:49 Submitted by: Chernowitz, Daniel Submitted to: SciPost Physics Core Academic field: Physics Specialties: Condensed Matter Physics - Theory 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, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential $n$-point correlation functions in the gas of GUE eigenvalues.

Published as SciPost Phys. 10, 071 (2021)

### List of changes

We have included more elaborate numerics, up to 8 qubits, for both the main results, and for a number of established numerical models, and have made the comparisons to the GUE and Poissonian ensembles more tangible. These numerics help tie the analytic averages to more concrete parts of physics.

We have mentioned connections to planar limits of diagrams.

We have made the comparisons explicit to existing limits in RMT and entanglement of random quantum states.

### Submission & Refereeing History

Resubmission 2001.00140v3 on 23 February 2021
Submission 2001.00140v2 on 8 January 2020

## Reports on this Submission

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The authors have modified the paper in a satisfactory manner.

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