Coexistence of long-range orders in a Bose-Holstein model

TL;DR

This paper investigates how superfluid and charge-density-wave states coexist or compete in a two-dimensional Bose-Holstein model with strong coupling, revealing conditions for supersolidity and phase separation through quantum Monte Carlo simulations.

Contribution

It provides a detailed analysis of phase coexistence in a Bose-Holstein model, highlighting the roles of double-hopping terms and coupling regimes in supersolidity and phase separation.

Findings

Checkerboard-supersolidity near half-filling

Phase separation when double-hopping is negligible

Dependence of phases on coupling strength and density

Abstract

Exploring supersolidity in naturally occurring and artificially designed systems has been and will continue to be an area of immense interest. Here, we study how superfluid and charge-density-wave (CDW) states cooperate or compete in a minimal model for hard-core-bosons (HCBs) coupled locally to optical phonons: a two-dimensional Bose-Holstein model. Our study is restricted to the parameter regimes of strong HCB-phonon coupling and non-adiabaticity. We use Quantum Monte Carlo simulation (involving stochastic-series-expansion technique) to study phase transitions and to investigate whether we have homogeneous or phase-separated coexistence. The effective Hamiltonian involves, besides a nearest-neighbor hopping and a nearest-neighbor repulsion, sizeable double-hopping terms (obtained from second-order perturbation). At densities not far from half-filling, in the parameter regime where the double-hopping terms are non-negligible (negligible) compared to the nearest-neighbor hopping, we get checkerboard-supersolidity (phase separation) with CDW being characterized by ordering wavevector $\vec{Q}=(\pi,\pi)$.