Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model

• Published in: arXiv.org
• Main Authors: Asadzadeh, Mohammad Zhian, Fabrizio, Michele, Arrigoni, Enrico
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 02.05.2016
• Subjects: Clusters; Equilibrium; Ising model; Mathematical models; Perturbation theory; Phase transitions; Physics - Strongly Correlated Electrons; Spin dynamics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1605.00472

We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the transverse magnetic field across the transition or within a phase. We treat both the one-dimensional case, for which an exact solution is available, as well the two-dimensional one, for which has to resort to numerical results. Comparison with exact results shows that the approach provides a quite accurate description of the real-time dynamics up to a characteristic time scale \(\tau\) that increses with the size of the cluster used for CPT. In addition, and not surprisingly \(\tau\) is small for quenches across the equilibrium phase transition, but can be quite larger for quenches within the ordered or disordered phases.