Permutation cycles of hardcore Bose-Hubbard models on square and Kagome lattices

TL;DR

This study investigates how permutation cycle statistics in hardcore Bose-Hubbard models on square and Kagome lattices can distinguish quantum phases and detect phase transitions, providing a new diagnostic tool.

Contribution

It introduces the use of permutation cycle statistics as a method to identify quantum phases and phase transitions in two-dimensional Bose-Hubbard models.

Findings

Permutation cycle features differentiate insulating phases.

Cycle length distributions detect superfluid-insulator transitions.

Permutation statistics correlate with local occupation resonances.

Abstract

In this paper, we study the statistics of permutation cycles of ground-state hardcore lattice bosons described by various two-dimensional Bose-Hubbard-type models on both square and Kagome lattices. We find that it is possible to differentiate quantum phases by the statistics of permutations cycles. Indeed, features in the permutation cycles statistics can be used to uniquely identify certain insulating phases, and are consistent with local resonances of occupation numbers in the ground-state expansion of the phase. We also confirm that suitable quantities derived from the probability distribution of the length of permutation cycles can be used to detect superfluid to insulator phase transitions.