Bose-Hubbard model with power-law hopping in one dimension

TL;DR

This study uses large-scale Quantum Monte Carlo simulations to explore the phase diagram of a one-dimensional Bose-Hubbard model with power-law hopping, revealing a new universality class for certain decay exponents and implications for long-range quantum systems.

Contribution

It provides the first detailed characterization of the phase transition and universality class in the 1D Bose-Hubbard model with power-law hopping, including critical exponents and spectrum analysis.

Findings

Continuous phase transition for 1<α≤3, incompatible with BKT.

Identification of a new universality class with specific critical exponents.

Behavior akin to higher-dimensional systems with long-range order for α≤2.

Abstract

We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/r^\alpha$ using exact large scale Quantum Monte-Carlo simulations. For all $1<\alpha\leq 3$ the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in a way incompatible with the Berezinskii-Kosterlitz-Thouless (BKT) scenario, which is recovered for $\alpha>3$. We characterise the new universality class by providing the critical exponents by means of data collapse analysis near the critical point for each $\alpha$ and from careful analysis of the spectrum. Large-scale simulations of the grand canonical phase diagram and of the decay of correlation functions demonstrate an overall behavior akin to higher dimensional systems with long-range order in the ground state for $\alpha \leq 2$ and intermediate between one and higher dimensions for $2<\alpha \leq 3$. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.