Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain

By M. Fagotti, M. Collura, F. Essler, Pasquale Calabrese. 2013

159 citations recorded by the source corpus.

We consider the time evolution after quantum quenches in the spin-1/2 Heisenberg XXZ quantum spin chain with Ising-like anisotropy. The time evolution of short-distance spin-spin correlation functions is studied by numerical tensor network techniques for a variety of initial states, including N\'eel and Majumdar-Ghosh states and the ground state of the XXZ chain at large values of the anisotropy. The various correlators appear to approach stationary values, which are found to be in good agreement with the results of exact calculations of stationary expectation values in appropriate generalized Gibbs ensembles. In particular, our analysis shows how symmetries of the post-quench Hamiltonian that are broken by particular initial states are restored at late times.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9f45b494fc83c04e414f18e8dde3e954009300fa

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. L. Vidmar
2. J. Caux
3. F. Essler
4. Marcos Rigol
5. M. Fagotti
6. Pasquale Calabrese
7. F. Borgonovi
8. Vladimir G. Zelevinsky

In Computational Mathematics

1. M. Fagotti
2. F. Essler

In Statistical and Nonlinear Physics

1. J. Caux
2. L. Vidmar
3. F. Essler
4. M. Fagotti
5. Marcos Rigol
6. Pasquale Calabrese
7. V. Alba
8. B. Doyon

Citations in the corpus

• Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, methodology): “sites [51, 63, 127], and initial states that are not necessarily pure [78], but are described by a density matrix ( ) ρ 0 .”
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles (2016, background): “While for integrable systems composed of non-interacting particles it is clear which conserved qu antities should be taken into account, for integrable syste m with interacting particles, such as the XXZ model, this is st ll an open question [266, 267, 268, 269, 270, 271].”
• The Quench Action (2016, background): “A GGE treatment including the traditional charges (those emanating from the usual ‘spin-1/2’ transfer matrix of the form (22), quasilocal charges not being known at the time) was proposed independently in [117] and [118] (the results of the latter subsequently extended in [119]).”
• Generalized Gibbs ensemble in integrable lattice models (2016, background): “Since then, the validity of the GGE to describe observables in integrable systems after equilibration has been demonstrated in a wide range of 1D models including: Luttinger liquids [39, 40, 41], the 1/r fermionic Hubbard model [42], the sine-Gordon model [43], the transverse field Ising model [44, ”