Scaling of fronts and entanglement spreading during a domain wall melting

TL;DR

This paper investigates the out-of-equilibrium dynamics of a one-dimensional XXZ spin chain during domain wall melting, revealing ballistic scaling, hydrodynamic behavior, and quantum fluctuation effects on entanglement spreading.

Contribution

It provides a comprehensive analysis combining exact lattice calculations, generalized hydrodynamics, and conformal field theory to describe entanglement and front dynamics in domain wall melting.

Findings

Ballistic scaling of conserved quantities with explicit functions

Hydrodynamic description of front dynamics via GHD

Quantum fluctuations influence entanglement spreading

Abstract

We revisit the out-of-equilibrium physics arising during the unitary evolution of a one-dimensional XXZ spin chain initially prepared in a domain wall state $\vert\psi_0\rangle=\vert\dots \uparrow\uparrow\downarrow\downarrow\dots\rangle$. In absence of interactions, we review the exact lattice calculation of several conserved quantities, including e.g. the magnetization and the spin current profiles. At large distances $x$ and times $t$, we show how these quantities allow for a ballistic scaling behavior in terms of the scaling variable $\zeta= x/t$, with exactly computable scaling functions. In such a limit of large space-time scales, we show that the asymptotic behavior of the system is suitably captured by the local occupation function of spinless fermionic modes, whose semi-classical evolution in phase space is given by a Euler hydrodynamic equation. Similarly, analytical results for the asymptotic fronts dynamics are obtained for the interacting chain via Generalized Hydrodynamics. In the last part of the work, we include large-scale quantum fluctuations on top of the semi-classical hydrodynamic background in the form of a conformal field theory that lives along the evolving Fermi contour. With this procedure, dubbed quantum generalized hydrodynamics, it is possible to obtain exact asymptotic results for the entanglement spreading during the melting dynamics.