Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice

TL;DR

This study maps the phase diagram of a combined SSH-Hubbard model on a square lattice, revealing a first-order transition from antiferromagnetic to bond-ordered phases driven by electron-phonon coupling.

Contribution

It provides the first detailed numerical phase diagram of the SSH-Hubbard model on a square lattice using determinant quantum Monte Carlo, highlighting the transition between AF and bond-ordered phases.

Findings

First-order transition between AF and bond-ordered phases.

Two distinct AF regions with different quantum fluctuation characteristics.

Phase diagram mapped out at half filling using sign-problem-free QMC.

Abstract

The Hubbard and Su-Schrieffer-Heeger Hamiltonians (SSH) are iconic models for understanding the qualitative effects of electron-electron and electron-phonon interactions respectively. In the two-dimensional square lattice Hubbard model at half filling, the on-site Coulomb repulsion, $U$, between up and down electrons induces antiferromagnetic (AF) order and a Mott insulating phase. On the other hand, for the SSH model, there is an AF phase when the electron-phonon coupling $\lambda$ is less than a critical value $\lambda_c$ and a bond order wave when $\lambda > \lambda_c$. In this work, we perform numerical studies on the square lattice optical Su-Schrieffer-Heeger-Hubbard Hamiltonian (SSHH), which combines both interactions. We use the determinant quantum Monte Carlo (DQMC) method which does not suffer from the fermionic sign problem at half filling. We map out the phase diagram and find that it exhibits a direct first-order transition between an antiferromagnetic phase and a bond-ordered wave as $\lambda$ increases. The AF phase is characterized by two different regions. At smaller $\lambda$ the behavior is similar to that of the pure Hubbard model; the other region, while maintaining long range AF order, exhibits larger kinetic energies and double occupancy, i.e. larger quantum fluctuations, similar to the AF phase found in the pure SSH model.