Energy transport between two integrable spin chains

Alberto Biella 1, 2 Andrea De Luca 3 Jacopo Viti 4 Davide Rossini 2, 1 Leonardo Mazza 5, 2 Rosario Fazio 6, 2, 1

Physical Review B : Condensed matter and materials physics, American Physical Society, 2016, 93, pp.205121

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 non-universal 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.

  • 1. Kavli Institute for Theoretical Physics
  • 2. SNS - Scuola Normale Superiore di Pisa
  • 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 4. UFRN - Universidade Federal do Rio Grande do Norte [Natal]
  • 5. Departement de Physique-ENS
  • 6. ICTP - International Center for Theoretical Physics [Trieste]