Superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors

TL;DR

This paper investigates the superfluid to Mott insulator quantum phase transition in the 1D Bose-Hubbard model at various integer fillings using numerical and analytical methods, providing critical points and transition conditions.

Contribution

It introduces a numerical approach to determine the transition point for arbitrary fillings and offers an analytical approximation for critical values across dimensions.

Findings

Critical points are accurately determined for various fillings.

The critical values follow a simple analytical function.

Conditions for transition points are discussed via instanton analysis.

Abstract

We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid to Mott insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a simple analytical function. We also discuss the condition for determining the transition point from a perspective of the instanton method.