Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54

TL;DR

This paper analyzes the non-equilibrium behavior of symmetry-resolved entanglement and entanglement asymmetry in the integrable Rule 54 cellular automaton, deriving exact asymptotics for charged moments using tensor network methods.

Contribution

It provides the first exact asymptotic expressions for symmetry-resolved entanglement measures in an interacting integrable model.

Findings

Charged moments decay exponentially with time.

Asymptotic form derived for large but finite times.

Tensor network approach enables analytical tractability.

Abstract

Symmetry resolved entanglement and entanglement asymmetry are two measures of quantum correlations sensitive to symmetries of the system. Here we discuss their non-equilibrium dynamics in the Rule 54 cellular automaton, a simple, yet interacting, integrable model. Both quantities can be expressed in terms of the more analytically tractable "charged moments", i.e. traces of powers of a suitably deformed density matrix, via a replica trick. We express them in terms of a tensor network, which we contract in space using a system of local algebraic relations. This gives the asymptotic form for the charged moments, valid in the regime of large but finite time that is shorter than all the relevant subsystem sizes. In this regime the charge moments decay exponentially with the rate given by the leading solution to a cubic equation.