Numerical Linked Cluster Expansions for Quantum Quenches in the Thermodynamic Limit

Studies of the quantum dynamics of isolated systems are providing fundamental insights into how statistical mechanics emerges under unitary time evolution. Thermalization seems ubiquitous, but experiments with ultracold gases have shown that it need not always occur. Unfortunately, computational studies of generic (quantum chaotic) models are limited to small systems, for which arbitrarily long times can be calculated, or short times, for which large or infinite system sizes can be solved. Consequently, what happens in the thermodynamic limit after long times has been inaccessible to theoretical studies. In this talk, we introduce a linked-cluster based computational approach that allows one to address the latter question in lattice systems. We use this approach to probe thermalization in quantum chaotic models and its breakdown at integrability [1,2], as well as to study quantum quenches and generalized thermalization in the integrable XXZ chain [3,4].

References
[1] M. Rigol. Quantum quenches in the thermodynamic limit. Phys. Rev. Lett. 112, 170601 (2014).
[2] M. Rigol. Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems. Phys. Rev. Lett. 116, 100601 (2016).
[3] B. Wouters, J. De Nardis, M. Brockmann, D. Fioretto, M. Rigol, and J.-S. Caux. Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble. Phys. Rev. Lett. 113, 117202 (2014).
[4] L. Piroli, E. Vernier, P. Calabrese, and M. Rigol. Correlations and diagonal entropy after quantum quenches in XXZ chains. Phys. Rev. B 95, 054308 (2017).