Non-ergodicity in Interacting Quasiperiodic Systems and Disordered Fock Lattice Models

Abstract

In this thesis, we study different aspects of many body localization in closed quantum systems. Many body localized systems are isolated interacting quantum systems that fail to thermalize on their own (non-ergodic) and thus violates the eigenstate thermalization hypothesis (ETH), which guarantees thermalization in quantum systems. These systems are known to have area law entanglement entropy even at high energy densities and have been argued to have emergent conservation laws, which prevent thermalization. The presence of thermal-MBL transitions has been confirmed in the interacting disordered systems and in the presence of deterministic quasiperiodic potentials, at least in one dimension. Initially, the MBL phase was introduced by showing that localization persists even in the presence of interactions in a system with a localized single particle spectrum. However, the fate of many body localization in interacting systems with coexisting localized and extended single particle states has been questioned recently and has been shown to be model-dependent. In the first work, we propose a dimensionless criterion based on the single particle spectrum, which can determine the presence or absence of the thermal-MBL transitions in the interacting quasiperiodic systems with coexisting localized and extended states. In the second work, we calculate the transport properties and the level spacing statistics in an interacting one dimensional system in the presence of similar quasiperiodic potential. The many-body spectrum of such a quasiperiodic system has been argued to have a non-ergodic extended phase, which is associated with the violation of ETH and volume law satisfying entanglement entropy. In this work, we show sub-diffusive transport in this non-ergodic extended phase in contrast to the diffusive transport in the thermal phase and no transport in the MBL phase. In the third work, we consider a tight-binding model in the Fock lattice with correlated onsite disorders and show the presence of a localization transition in such Fock lattice models. We consider different functional forms of correlations for the onsite Fock lattice potentials keeping the effective disorder strength fixed and discuss the possibility of localization transitions driven by the correlation among the onsite terms. In the fourth work, we develop a recursive method to calculate the exact Green’s functions in the Fock lattice, where each slice of the Fock lattice is added in recursion while calculating different elements of the total Green’s function. Using this method, we calculate different quantities to locate the thermal-MBL transition in interacting disordered systems as an alternative to the exact diagonalization method typically used in studies of MBL systems.