Exact duality and dual Monte-Carlo simulation for the Bosonic Hubbard model

TL;DR

This paper derives an exact dual formulation of the Bosonic Hubbard model, enabling efficient Monte Carlo simulations and improved measurement of correlation functions, with new results for 1D and 2D models.

Contribution

The paper presents the first exact dual representation of the Bosonic Hubbard model, including the hard core case, and develops a novel Monte Carlo algorithm for improved measurements.

Findings

Efficient Monte Carlo algorithm for the dual model

Accurate measurement of Green functions

New results for zero mode filling in 2D hardcore model

Abstract

We derive the exact dual to the Bosonic Hubbard model. The dual variables take the form of conserved current loops (local and global). Previously this has been done only for the very soft core model at very high density. No such approximations are made here. In particular, the dual of the hard core model is shown to have a very simple form which is then used to construct an efficient Monte Carlo algorithm which is quite similar to the World Line algorithm but with some important differences. For example, with this algorithm we can measure easily the correlation function of the order parameter (Green function), a quantity which is extremely difficult to measure with the standard World Line algorithm. We demonstrate the algorithm for the one and two dimensional hardcore Bosonic Hubbard models. We present new results especially for the Green function and zero mode filling fraction in the two dimensional hardcore model.