Stability of current-carrying states in hard-core bosons with long-range hopping on a square lattice

TL;DR

This paper studies how long-range hopping affects the stability of current-carrying states in a hard-core Bose-Hubbard model on a square lattice, revealing critical behaviors and instabilities related to the decay exponent of hopping.

Contribution

It provides a mean-field analysis of the excitation spectrum and identifies how long-range hopping influences the critical quasi-momenta for instabilities, especially near the decay exponent $oldsymbol{ ext{α=3}}$.

Findings

Critical quasi-momenta vanish at α=3.

Long-range hopping suppresses stability, leading to instabilities.

Scaling behavior of critical quasi-momentum near α=3.

Abstract

We investigate the stability of current-carrying states with quasi-momentum $K$ in the Bose-condensed phase of the hard-core Bose-Hubbard model on a square lattice, where particles transfer between two sites separated by distance $r$ with hopping amplitude decaying algebraically with $r$ as $\propto r^{-\alpha}$. Using a mean-field theory, we analyze the excitation spectrum and determine the critical quasi-momenta associated with Landau and dynamical instabilities. We find that the long-range hopping suppresses the critical quasi-momenta and makes them vanish at $\alpha=3$. Near $\alpha=3$, we show that the critical quasi-momentum $K_{\mathrm{c}}$ for the dynamical instability exhibits the scaling behavior $K_\mathrm{c} \propto \Delta^{1+\Delta}$ with $\Delta=\alpha-3$, where the scaling exponent explicitly depends on $\Delta$, as a consequence of the long-range nature of the hopping.