Phase Properties of Interacting Bosons in Presence of Quasiperiodic and Random Disorder

TL;DR

This study compares the phase properties of interacting bosons in two-dimensional lattices under quasiperiodic and random disorder, revealing unique phases and critical behaviors through mean-field and finite-size scaling analyses.

Contribution

It introduces a detailed comparison of disorder effects on bosonic phases, including the discovery of a new mixed phase specific to quasiperiodic disorder and analyzes their critical properties.

Findings

Quasiperiodic disorder stabilizes the Bose-glass phase more effectively.

A new mixed phase (QM) appears under quasiperiodic disorder.

Critical exponents for phase transitions align with quantum Monte Carlo results.

Abstract

Motivated by two different types of disorder that occur in quantum systems with ubiquity, namely, the random and the quasiperiodic (QP) disorder, we have performed a systematic comparison of the emerging phase properties corresponding to these two cases for a system of interacting bosons in a two dimensional square lattice. Such a comparison is imperative as a random disorder at each lattice is completely uncorrelated, while a quasiperiodic disorder is deterministic in nature. Using a site decoupled mean-field approximation followed by a percolation analysis on a BoseHubbard model, several different phases are realized, such as the familiar Bose-glass (BG), Mott insulator (MI), superfluid (SF) phases, and, additionally, we observe a mixed phase, specific to the QP disorder, which we call as a QM phase. Incidentally, the QP disorder stabilizes the BG phase more efficiently than the case of random disorder. Further, we have employed a finite-size scaling analysis to characterize various phase transitions via computing the critical transition points and the corresponding critical exponents. The results show that for both types of disorder, the transition from the BG phase to the SF phase belongs to the same universality class. However, the QM to the SF transition for the QP disorder comprises of different critical exponents, thereby hinting at the involvement of a different universality class therein. The critical exponents that depict all the various phase transitions occurring as a function of the disorder strength are found to be in good agreement with the quantum Monte-Carlo results available in the literature.