Mixed-State Entanglement in a Minimal Model of Quantum Chaos

TL;DR

This paper investigates the dynamics of mixed-state entanglement in a quantum chaotic model, deriving exact spectral relations and demonstrating how entanglement measures evolve and saturate in different partition scenarios.

Contribution

It introduces an exact spectral analysis of the partially transposed density matrix in a quantum chaos model, revealing relations between entanglement measures and their late-time behavior.

Findings

Exact spectrum of the partially transposed density matrix obtained.

Entanglement measures saturate to Haar-random values at late times for equal partitions.

R\'enyi mutual information and negativity vanish at late times for unequal partitions.

Abstract

Understanding the dynamics of quantum correlations in many-body systems is a central problem in non-equilibrium quantum physics. We study the spread of mixed-state entanglement in a minimal model of quantum chaos, the kicked field Ising model. By combining the replica trick with the space-time duality of the model, we determine the exact spectrum of the partially transposed reduced density matrix. The resulting flat spectrum leads to exact relations between entanglement negativity, odd entropy and R\'enyi mutual information at early times. Numerical results further demonstrate that for equal tri-partitions and at late times, all entanglement measures saturate to the Haar-random values. In contrast, for unequal tri-partitions R\'enyi mutual information and negativity vanish at late times, implying that the corresponding reduced density matrix is factorizable. Extensive numerical simulations also show that the relation remains quantitatively valid for generic initial states, leading us to conjecture it for all initial states and all times.