Physics Department - Quantum Critical States in Quasiperiodic Lattices: A Unified Framework

Abstract

The disordered quantum systems host three types of fundamental quantum states, the extended, localized, and critical states, of which the multifractal critical states are much less understood compared with the former two. Conventionally the characterization of the quantum critical states relies on arduous numerical verification. In this talk, I will present a systematic analytic and numerical study of the critical states in quasiperiodic systems, with or without particle-particle interactions. Through the Avila global theory, a Fields Medal work which we introduce for the first time to cold atoms, we propose a class of exactly solvable models, dubbed quasiperiodic mosaic lattice models, hosting novel types of exact mobility edges separating localized from quantum critical or extended states, With these exactly solvable models, we discover a universal mechanism for the critical states that the such states are due to the vanishing Lyapunov exponent and the incommensurately distributed hopping zeros in the thermodynamic limit, which also serve as a rigorous characterization of the critical states. We further extend the mechanism of the critical states to a broad regime, in which we predict the existence of seven fundamental localization phases in disordered systems, and establish a unified framework to characterize such phases. In particular, an exact theory is presented to understand all the seven fundamental localization quantum phases. Finally, we show that in the presence of interactions, the critical states turn into the many-body counterparts upon the finite-size scaling analysis, giving a many-body critical phase, which is an exotic phase in-between the thermal phase and many-body localization. We also discuss our latest experimental realization of the present predictions. Future important issues will be commented.