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

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, |down arrow... up down arrow ... up down arrow ... down arrow >. 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.

Automated summary

In this study, we investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime |Delta| < 1. We find that two domain walls in the initially prepared state with two domain walls exhibit independent evolution at early times, and only after a calculable time do they start to interact, resulting in the occurrence of a split Fermi sea. For Delta = 0, we derive exact asymptotic results for the magnetization and the spin current using a semi-classical Wigner function approach, and we accurately determine the spreading of entanglement entropy using quantum fluctuating hydrodynamics tools. In the interacting case, we analytically solve the Generalized Hydrodynamics equation, providing exact expressions for the conserved quantities. We also present numerical results for the entanglement entropy in the interacting case and propose a conjecture for its asymptotic value.