2015/04/30 by Vipin Kerala Varma, Sebastiano Pilati · 1 citation
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.quant-gas
paper · pdf · doi:10.1103/physrevb.92.134207
published as Phys. Rev. B 92, 134207 (2015) · Previous final section on 3D noninteracting Anderson model is replaced by study of an interacting Aubry-Andre chain, motivated by recent experiments and to reinforce the narrative. Title changed correspondingly
arxiv created 2015/10/16 · arxiv updated 2015/10/19
Understanding the metal-insulator transition in disordered many-fermion systems, both with and without interactions, is one of the most challenging and consequential problems in condensed matter physics. In this paper we address this issue from the perspective of the modern theory of the insulating state (MTIS), which has already proven to be effective for band and Mott insulators in clean systems. First we consider noninteracting systems with different types of aperiodic external potentials: uncorrelated disorder (one-dimensional Anderson model), deterministic disorder (Aubry-André Hamiltonian and its modification including next-nearest neighbour hopping), and disorder with long-range correlations (self-affine potential). We show how the many-body localisation tensor defined within the MTIS may be used as a powerful probe to discriminate the insulating and the metallic phases, and to locate the transition point. Then we investigate the effect of weak repulsive interactions in the Aubry-André Hamiltonian, a model which describes a recent cold-atoms experiment. By treating the weak interactions within a mean-field approximation we obtain a linear shift of the transition point towards stronger disorder, providing evidence for delocalisation induced by interactions.