Professor Fabian Essler

Abstract:

We employ equation of motion techniques to study the non-equilibrium dynamics in a lattice model of weakly interacting spinless fermions. Our model provides a simple setting for analyzing the effects of weak integrability breaking perturbations on the time evolution after a quantum quench. We establish the accuracy of the method by comparing results at short and intermediate times to time-dependent density matrix renormalization group computations. For sufficiently weak integrability-breaking interactions we always observe prethermalization plateaux, where local observables relax to non-thermal values at intermediate time scales. At later times a crossover towards thermal behaviour sets in. We determine the associated time scale, which depends on the initial state, the band structure of the non-interacting theory, and the strength of the integrability breaking perturbation. Our method allows us to analyze in some detail the spreading of correlations and in particular the structure of the associated light cones in our model. We find that the interior and exterior of the light cone are separated by an intermediate region, the temporal width of which appears to scale with a universal power-law $t^{1/3}$.

Abstract:

We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the sense of Grover & Fisher (2014 J. Stat. Mech.2014, P10010. (doi:10.1088/1742-5468/2014/10/P10010)). These states are atypical in the sense that their entropy density is smaller than that of thermal states at the same energy density. Furthermore, we show that thermal states in a particular temperature window exhibit a weaker form of the QDL property, in agreement with recent results obtained by strong-coupling expansion methods in Veness et al. (2016 (http://arxiv.org/abs/1611.02075)).This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.