Phases and Exotic Phase Transitions of a Two-Dimensional Su-Schrieffer-Heeger Model

Abstract

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 ${\omega }_0$. 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 $\pi$ 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 $(\pi ,0)$ valence bond solid (VBS) and an antiferromagnetic (AFM) phase with increasing ${\omega }_0$. For large $t$ and small ${\omega }_0$, we find finite-temperature signatures, a disordered pseudogap phase, of a previously reported $(\pi ,\pi )$ VBS ground state related to a nesting instability. With increasing ${\omega }_0$, AFM order again emerges.

17 pages, 19 figures

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• Spin-Peierls instability of deconfined quantum critical points
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• Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment
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