Energy transport between two integrable spin chains
Year: 2016
Authors: Biella A., De Luca A., Viti J., Rossini D., Mazza L., Fazio R.
Autors Affiliation: Scuola Normale Super Pisa, NEST, Piazza Cavalieri 7, I-56126 Pisa, Italy; CNR, Ist Nanosci, I-56126 Pisa, Italy; Univ Calif Santa Barbara, Kavli Inst Theoret Phys, Santa Barbara, CA 93106 USA; Univ Paris Saclay, Univ Paris 11, CNRS, LPTMS, F-91405 Orsay, France; Campos Univ, Escola Ciencia & Tecnol UFRN, BR-59078970 Lagoa, Natal, Brazil; PSL Res Univ, Ecole Normale Super, Dept Phys, CNRS, 24 Rue Lhomond, F-75005 Paris, France; Abdus Salaam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy.
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 bosonization and time-dependent matrix-product-state simulations, the different contributions of low-lying bosonic modes and of fermionic quasiparticles 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 picture that emerges is the following. Since integrability is only locally broken in this model, a preequilibration behavior 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. Thermalization, characterized by the absence of any energy flow, occurs only on longer time scales which are not accessible with our numerics.
Journal/Review: PHYSICAL REVIEW B
Volume: 93 (20) Pages from: 205121-1 to: 205121-13
More Information: We acknowledge enlightening discussions with J. Dubail, M. Haque, J. E. Moore, J.-.M. Stephan, and X. Zotos. A.B., D.R., L.M., and R.F. acknowledge the Kavli Institute for Theoretical Physics, University of California, Santa Barbara (USA), for the hospitality and support during the completion of this work. This work was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915, by Investissements d’Avenir LabEX PALM (Grant No. ANR-10-LABX-0039-PALM)(A.D.), by LabEX ENS-ICFP: Grant No. ANR-10-LABX-0010/ANR-10-IDEX-0001-02 PSL* (L.M.), by EU (IP-SIQS) and (STREP-QUIC) (R.F.), by the Italian MIUR (FIRB Project No. RBFR12NLNA) (D.R.), and by Scuola Normale Superiore through the internal project Non-equilibrium dynamics of one-dimensional quantum systems (R.F., D.R., and L.M.).KeyWords: Matrix Renormalization-group; Thermal Transport; Quantum Wires; Steady-states; SystemsDOI: 10.1103/PhysRevB.93.205121Citations: 59data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)