Transport, localization and entanglement in disordered and interacting systems: From real space to Fock space

Abstract

In this thesis, we explore some of the exciting physics of condensed matter systems manifested because of imperfection or disorder and interactions among the constituent particles. In phenomena like transport, e.g., electrical current; localization, e.g., confinement of electrons only within a small part of a system; entanglement (a correlation among the constituents particle); disorder and interaction play essential roles. These three properties are our main focus in the thesis. There are six chapters. In the first chapter, we introduce a few landmarks in the field to set the stage and give an overview of the works presented in the thesis. In the second chapter, we consider quasi-disordered or quasiperiodic systems in one, two, and three dimensions, where the quasi-disorder is deterministic but non-repeating throughout a lattice and considered from. Metal-insulator transitions in these systems are probed by calculating conductances and their change with system size. More specifically, we look at the systems from the perspective of single-parameter scaling theory. In the third chapter, we consider both the disordered and quasi-disordered systems with interactions. The systems show transitions from thermal to many-body localized phases, and we study them in Fock space, which is a natural description for an interacting system. We exploit the Fock space structure to calculate the propagator or Green’s function in an iterative way to push the system size accessible in the exact calculations. We define a length scale in Fock space, which can detect the phase transition and distinguish between the disordered and the quasi-disordered systems. In the fourth chapter, motivated by an experiment, we study the electrical current and noise therein in a disordered quantum Hall system in the proximity of a superconductor. To our surprise, the quantum Hall conductance plateau in the system comes with noise in the current as also observed in the experiment, and the calculated quantities match pretty well with the observed values. In the fifth chapter, we study the entanglement entropy of an interacting fermionic system using a new saddle-point approximation similar to a mean-field approximation. The approximation is based on a newly developed path integral approach for calculating the entanglement entropy. In the last chapter, we conclude the thesis by summarizing the important findings of our works presented in the thesis with some future directions.