2016/06/30 by Lorenzo Piroli, Eric Vernier, Pasquale Calabrese
Mathematics · Physics and Astronomy · #Bethe ansatz #Eigenvalues and eigenvectors #Ferromagnetism #Hamiltonian (control theory) #Heisenberg model #Integrable system #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Stationary state #Statistical physics #Tensor decomposition and applications #Time evolution #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.94.054313
published as Phys. Rev. B 94, 054313 (2016) · 25 pages, 11 figures; v2: minor revision and appendix added
openalex created_date 2016/06/24 · arxiv created 2016/08/11 · openalex publication_date 2016/08/23 · arxiv updated 2016/08/24 · openalex updated_date 2026/08/05
What is the long-time behavior of a quantum system after it is brought out of equilibrium? In a generic case, it has been proposed that an effective thermalization occurs, and the local properties of the system can then be described by a thermal Gibbs ensemble. However, in integrable systems, with infinitely many conservation laws, the answer is far more complicated. It was shown in several special cases that the long-time steady state can be exactly described by the so called complete generalized Gibbs ensemble. The latter can be obtained by maximizing the entropy with constraints imposed by the conservation of energy, but also by additional carefully chosen subset of the integrals of motion. In this work, the authors analyze more general initial states, focusing on integrable XXZ Heisenberg spin chains. They find that the complete generalized Gibbs ensemble indeed correctly describes the system at long times after the quench.