Entanglement dynamics of many-body quantum states: sensitivity to system conditions and a hidden universality

TL;DR

This paper develops a unified mathematical framework to analyze how bipartite entanglement entropy evolves in many-body quantum states, revealing a hidden universality across different system conditions.

Contribution

It introduces a single-parameter formulation for entanglement dynamics in Gaussian ensemble Hamiltonians, connecting various quantum states through a common mathematical description.

Findings

Derived state ensembles for eigenstates of Gaussian Hamiltonians.

Identified a single functional parameter governing entanglement evolution.

Uncovered a hidden universality linking different quantum states.

Abstract

We consider physical Hamiltonians that can be represented by the multiparametric Gaussian ensembles, theoretically derive the state ensembles for its eigenstates and analyze the effect of varying system conditions on its bipartite entanglement entropy. Our approach leads to a single parametric based common mathematical formulation for the evolution of the entanglement statistics of different states of a given Hamiltonian or different Hamiltonians subjected to same symmetry constraints. The parameter turns out to be a single functional of the system parameters and thereby reveals a deep web of connection hidden underneath different quantum states.