Bound states in one-dimensional systems with colored noise

TL;DR

This paper explores phase transitions in a one-dimensional system with colored noise, revealing a new bound phase characterized by localized wave functions and coexistence with extended states, refining the understanding of phase diagrams.

Contribution

It introduces the concept of a bound phase in 1D systems with colored noise, showing its coexistence with extended states and distinguishing it from Anderson localization.

Findings

Identification of a bound phase with non-exponentially decaying tails

Coexistence of bound and extended states in the spectrum

Discrepancy between static and dynamic transition points for large noise correlation

Abstract

We investigate the phase transitions in a one-dimensional system with colored noise. Previous studies indicated that the phase diagram of this system included extended and disorder-induced localized phases. However, by studying the properties of wave functions, we find that this phase diagram can be further refined, revealing the existence of a bound phase for the large potential amplitude $W$ and noise control parameter $\alpha$. In the bound phase, the wave function cannot extend throughout the entire chain, tails decay faster than exponentially and its distribution expands as the system size increases. By adjusting the potential amplitude to induce a transition from the extended phase to the bound phase, we find that bound states coexist with extended states in the spectrum. In contrast, when the system transitions from the Anderson localized phase to the bound phase, we do not observe the obvious coexistence of Anderson localized and bound states. Finally, by performing the time evolution, we find that the dynamic transition point of the bound phase is inconsistent with the static one for large $\alpha$.