Energy transport between two integrable spin chains

Abstract

We study the energy transport in a system of two half-infinite XXZ chains initially kept separated at different temperatures, and later connected and let free to evolve unitarily. By changing independently the parameters of the two halves, we highlight, through bosonisation and time-dependent matrix-product-state simulations, the different contributions of low-lying bosonic modes and of fermionic quasi-particles to the energy transport. In the simulations we also observe that the energy current reaches a finite value which only slowly decays to zero. The general pictures that emerges is the following. Since integrability is only locally broken in this model, a pre-equilibration behaviour may appear. In particular, when the sound velocities of the bosonic modes of the two halves match, the low-temperature energy current is almost stationary and described by a formula with a nonuniversal prefactor interpreted as a transmission coefficient. Thermalisation, characterized by the absence of any energy flow, occurs only on longer time-scales which are not accessible with our numerics.

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

“…Similar results were obtained in the framework of conformal field theory and Luttinger liquid descriptions [25][26][27][28][29][30][31][32][33][34][35][36][37]. In the presence of interactions the situation was less clear [38][39][40][41][42][43][44][45][46][47], but, eventually, Refs [48,49] have shown that the continuity equations satisfied by the (quasi)local conserved quantities are sufficient to characterize the late-time behavior. The framework developed in Refs [48,49] is now known as generalized hydrodynamics [48], where "generalized" is used to emphasize that integrable models have infinitely many (quasi)local charges [50].…”

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

“…Groundbreaking cold-atom experiments have also investigated several aspects of the coherent dynamics of closed quantum many-body systems [16][17][18][19][20][21][22][23][24]. These research efforts allowed to faithfully address how the presence of impurities and inhomogeneities may affect the quantum transport phenomena, also far from the linearresponse regime [25][26][27][28][29].As a paradigmatic example, we study a setup composed of two different semi-infinite spin-1/2 chains connected through a junction at x = 0 (see Fig. 1) [27].…”

“…These research efforts allowed to faithfully address how the presence of impurities and inhomogeneities may affect the quantum transport phenomena, also far from the linearresponse regime [25][26][27][28][29].As a paradigmatic example, we study a setup composed of two different semi-infinite spin-1/2 chains connected through a junction at x = 0 (see Fig. 1) [27]. In order to highlight the resistive effects taking place at the junction, we consider two models for which ballistic transport of spin and energy has been unambiguously demonstrated.…”

Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem

“…Inhomogeneous quenches, in general, pose a more difficult problem than homogeneous ones with fewer exact or approximate results [28][29][30][31][32][33][34][35][36]. One promising approach exploits hydrodynamical description assuming the separation of spatial and temporal scales and a local (GGE) equilibrium, and is supported both by numerical simulations and experimental observations [37][38][39][40][41].…”