Study of supersolidity in the two-dimensional Hubbard-Holstein model

TL;DR

This study derives an effective Hamiltonian for the 2D Hubbard-Holstein model under strong interactions, revealing a supersolid phase at certain fillings through quantum Monte Carlo simulations.

Contribution

It introduces a nonperturbative derivation of an effective Hamiltonian and uncovers supersolid phases in the two-dimensional Hubbard-Holstein model.

Findings

Identification of a supersolid phase around 1/8 filling.

First-order transition from superfluid to striped solid at certain interactions.

Observation of valence bond solid and phase separation at other fillings.

Abstract

We derive an effective Hamiltonian for the two-dimensional Hubbard-Holstein model in the regimes of strong electron-electron and strong electron-phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a $t_1-V_1-V_2-V_3$ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling $1/8$, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector $\vec{Q}=(\pi/4,3\pi/4)$ or $(\pi/4,5\pi/4)$. Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling $1/8$ and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.