Describing many-body localized systems in thermal environments. (20th June 2019)

• Record Type: Journal Article
• Authors: Wu, Ling-Na; Schnell, Alexander; Tomasi, Giuseppe De; Heyl, Markus; Eckardt, André
• Is Part Of: New journal of physics. Volume 21:Number 6(2019:Jun.)
• Publication Date: 2019-06-20
• Subjects: many body localization -- thermal environment -- Lindblad master equation -- variable range hopping -- quantum-jump Monte Carlo -- kinetic theory; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/ab25a4
• Languages: English
• ISSNs: 1367-2630

Abstract

Abstract: In this work we formulate an efficient method for the description of fully many-body localized systems in weak contact with thermal environments at temperature T . The key idea is to exploit the representation of the system in terms of quasi-local integrals of motion ( l -bits) to efficiently derive the generator for the quantum master equation in Born–Markov approximation. We, moreover, show how to compute the steady state of this equation efficiently by using quantum-jump Monte-Carlo techniques as well as by deriving approximate kinetic equations of motion. As an example, we consider a one-dimensional disordered extended Hubbard model for spinless fermions, for which we derive the l -bit representation approximately by employing a recently proposed method valid in the limit of strong disorder and weak interactions. Coupling the system to a global thermal bath, we study the transport between two leads with different chemical potentials at both of its ends. We find that the temperature-dependent current is captured by an interaction-dependent version of Mott's law for variable range hopping, where transport is enhanced/lowered depending on whether the interactions are attractive or repulsive, respectively. We interpret these results in terms of spatio-energetic correlations between the l -bits.