TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.10.3.071
TI  - Entanglement Dynamics of Random GUE Hamiltonians
PY  - 2021/03/19
UR  - https://scipost.org/SciPostPhys.10.3.071
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 10
IS  - 3
SP  - 071
A1  - Chernowitz, Daniel
AU  - Gritsev, Vladimir
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.10.3.071,
	title={{Entanglement Dynamics of Random GUE Hamiltonians}},
	author={Daniel Chernowitz and Vladimir Gritsev},
	journal={SciPost Phys.},
	volume={10},
	pages={071},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.10.3.071},
	url={https://scipost.org/10.21468/SciPostPhys.10.3.071},
}