The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model

TL;DR

This paper investigates the phase transition in the two-dimensional boson Hubbard model at incommensurate chemical potential, revealing it is second order in the thermodynamic limit despite finite-size indications of first order behavior.

Contribution

It demonstrates that the apparent first order transition in finite systems is a finite-size effect, establishing the transition as second order in the thermodynamic limit.

Findings

Multi-peak energy distribution in finite lattices suggests first order transition.

Multi-peak structure disappears in the thermodynamic limit, indicating second order transition.

Results challenge previous assumptions about disorder relevance at this transition.

Abstract

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.