We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought of as the result of joining chains with different global properties. Through dephasing, at late times, the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: (1) at different temperatures, (2) in the ground state of two different models, and (3) in the "domain wall" state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on time-evolving block decimation algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.

Transport in Out-of-EquilibriumXXZ Chains: Exact Profiles of Charges and Currents / Bertini, Bruno; Collura, Mario; De Nardis, Jacopo; Fagotti, Maurizio. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 117:20(2016), pp. 1-8. [10.1103/PhysRevLett.117.207201]

Transport in Out-of-EquilibriumXXZ Chains: Exact Profiles of Charges and Currents

Bertini, Bruno;Collura, Mario;De Nardis, Jacopo;Fagotti, Maurizio
2016

Abstract

We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought of as the result of joining chains with different global properties. Through dephasing, at late times, the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: (1) at different temperatures, (2) in the ground state of two different models, and (3) in the "domain wall" state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on time-evolving block decimation algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.
117
20
1
8
207201
https://arxiv.org/abs/1605.09790
Bertini, Bruno; Collura, Mario; De Nardis, Jacopo; Fagotti, Maurizio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/103446
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