Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model

TL;DR

This paper uses advanced numerical methods to precisely locate the superfluid-Mott insulator transition in the 1D Bose-Hubbard model by analyzing the gap, fidelity susceptibility, and Bloch oscillations, with implications for ultracold gas experiments.

Contribution

It introduces a generic scaling procedure for the gap and demonstrates Bloch oscillations as a novel experimental probe for the phase transition.

Findings

Critical points determined with high accuracy.

Fidelity susceptibility behavior across the transition.

Bloch oscillation amplitude vanishes at critical points.

Abstract

We investigate the interaction-induced superfluid-to-Mott insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.