Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model

TL;DR

This paper provides an exact hydrodynamic solution for the non-equilibrium evolution of a spin-1/2 XXZ chain with double domain walls, revealing detailed dynamics, entanglement growth, and conserved quantities in both free and interacting regimes.

Contribution

It offers the first exact hydrodynamic analysis of double domain wall melting in the XXZ model, including asymptotic magnetization, spin current, and entanglement entropy results.

Findings

Exact asymptotic magnetization and spin current for Δ=0

Analytical solutions for conserved quantities via Generalized Hydrodynamics

Numerical and conjectured results for entanglement entropy growth

Abstract

We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|\Delta|< 1$, initially prepared in a product state with two domain walls i.e, $|\downarrow\dots\downarrow\uparrow\dots\uparrow\downarrow\dots\downarrow\rangle$. At early times, the two domain walls evolve independently and only after a calculable time a non-trivial interplay between the two emerges and results in the occurrence of a split Fermi sea. For $\Delta=0$, we derive exact asymptotic results for the magnetization and the spin current by using a semi-classical Wigner function approach, and we exactly determine the spreading of entanglement entropy exploiting the recently developed tools of quantum fluctuating hydrodynamics. In the interacting case, we analytically solve the Generalized Hydrodynamics equation providing exact expressions for the conserved quantities. We display some numerical results for the entanglement entropy also in the interacting case and we propose a conjecture for its asymptotic value.