Quantum phase transition in Bose-Holstein model in two dimensions

TL;DR

This paper investigates quantum phase transitions in a two-dimensional Bose-Holstein model, revealing superfluid, supersolid, and charge-density-wave phases depending on filling and coupling, supported by extensive numerical analysis.

Contribution

It derives an effective Hamiltonian showing how next-nearest-neighbor hopping induces specific phase transitions, including a first-order superfluid-to-supersolid transition.

Findings

Superfluid-to-supersolid transition at intermediate couplings with next-nearest-neighbor hopping.

Phase separation occurs at strong couplings.

Superfluid-to-charge-density-wave transition at half-filling without supersolidity.

Abstract

We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. Away from half-filling, we show that the presence of next-nearest-neighbor hopping in the effective Hamiltonian leads to a superfluid-to-supersolid transition at intermediate boson-phonon (b-p) couplings, while at strong-couplings the system phase separates. However, at half-filling and at a critical b-p coupling (as in the xxz-model), the system undergoes a superfluid-to-charge-density-wave transition without any signature of supersolidity. Our analyses is based on extensive calculations of the structure factor, the superfluid fraction, the Bose-Einstein condensate fraction, and the system energy at various fillings. We present a phase diagram for this system and compare it to that of the xxz-model. We also demonstrate explicitly that the next-nearest-neighbor hopping (in the absence of nearest-neighbor hopping) in the effective Hamiltonian leads only to a single transition, i.e., a first-order superfluid-to-supersolid transition.