Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model
We study a Su-Schrieffer-Heeger electron-phonon model on a square lattice by means of auxiliary-field quantum Monte Carlo simulations. The addition of a symmetry-allowed interaction permits analytical integration over the phonons at the expense of discrete Hubbard-Stratonovich fields with imaginary-time correlations. Using single-spin-flip and global updates, we investigate the phase diagram at the O(4)-symmetric point as a function of hopping $t$ and phonon frequency $ω_0$. For $t=0$, where electron hopping is boson assisted, the model maps onto an unconstrained $\mathbb{Z}_2$ gauge theory. A key quantity is the emergent effective flux per plaquette, which equals $π$ in the assisted-hopping regime and vanishes for large $t$. Phases in the former regime can be understood in terms of instabilities of emergent Dirac fermions. Our results support a direct and continuous transition between a $(π,0)$ valence bond solid (VBS) and an antiferromagnetic (AFM) phase with increasing $ω_0$. For large $t$ and small $ω_0$, we find finite-temperature signatures, a disordered pseudogap phase, of a previously reported $(π,π)$ VBS ground state related to a nesting instability. With increasing $ω_0$, AFM order again emerges.