SciPost Submission Page
Entanglement Dynamics of Random GUE Hamiltonians
by Daniel Chernowitz, Vladimir Gritsev
|As Contributors:||Daniel Chernowitz|
|Submitted by:||Chernowitz, Daniel|
|Submitted to:||SciPost Physics|
|Subject area:||Quantum Physics|
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.