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arXiv:2102.08899 · Physical review. B./Physical review. B

Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics

Anika Götz, Stefan Beyl, Martin Hohenadler, Fakher F. Assaad

Published Feb 28, 2022• 51 citations
arXivHTMLPDF

Abstract

Electron-phonon coupling is typically not associated with magnetic order but with either charge density waves (patterns of high and low electron density) or valence-bond solids (patterns of strong and weak electronic bonds). Using quantum Monte Carlo simulations, the authors demonstrate that, within the paradigmatic two-dimensional Su-Schrieffer-Heeger model, the electron-phonon interaction favors antiferromagnetic order in large regions of the phase diagram. A valence-bond solid is observed in the adiabatic regime, while the two phases are connected by an apparently direct phase transition.

DOI
10.1103/physrevb.105.085151

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Electron-phonon coupling is typically not associated with magnetic order but with either charge density waves (patterns of high and low electron density) or valence-bond solids (patterns of strong and weak electronic bonds). Using quantum Monte Carlo simulations, the authors demonstrate that, within the paradigmatic two-dimensional Su-Schrieffer-Heeger model, the electron-phonon interaction favors antiferromagnetic order in large regions of the phase diagram. A valence-bond solid is observed in the adiabatic regime, while the two phases are connected by an apparently direct phase transition.
Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.
Most nonperturbative numerical studies of electron-phonon interactions focus on model Hamiltonians where the electrons interact with a phonon branch via a single type of microscopic mechanism. Two commonly explored couplings in this context are the Holstein and Su-Schrieffer-Heeger (SSH) interactions, which describe phonons modulating the on-site energy and intersite electron hopping, respectively. Many materials, however, have multiple phonon branches that can each interact with electronic degrees of freedom in different ways. We present here a determinant quantum Monte Carlo study of the half-filled two-dimensional (bond) SSH-Holstein Hamiltonian, where electrons couple to different phonon branches via either the Holstein or SSH mechanism. We map the model's phase diagram and determine the nature of the transitions between charge-density wave, bond-order wave, and antiferromagnetic order.
We use Langevin sampling methods within the auxiliary-field quantum Monte Carlo algorithm to investigate the phases of the Su-Schrieffer-Heeger model on the square lattice at the O(4) symmetric point. Based on an explicit determination of the density of zeros of the fermion determinant, we argue that this method is efficient in the adiabatic limit. By analyzing dynamical and static quantities of the model, we demonstrate that a (π,π)(\pi,\pi)(π,π) valence bond solid gives way to an antiferromagnetic phase with increasing phonon frequency.
We recently unveiled that antiferromagnetism (AFM) order can be dominantly induced by the bond Su-Schrieffer-Heeger (SSH) electron-phonon coupling (EPC), which is beyond the conventional wisdom that AFM order is usually driven by strong Coulomb interactions. Nevertheless, many aspects of the interplay between EPC and strong electronic interactions on AFM ordering remain unexplored. Here, we investigate the Su-Schrieffer-Heeger-Hubbard (SSHH) model with bond SSH phonons and on-site Hubbard interactions by large-scale quantum Monte Carlo (QMC) simulations and obtain its ground-state phase diagram for various Hubbard interactions and EPC strength at half filling. Our results show that Hubbard interactions further enhance EPC-induced AFM, especially for small phonon frequency or in adiabatic limit, the regime most relevant to various quantum materials. This could shed further light to understanding the cooperative effect between EPC and electronic correlations in quantum materials.
The Su-Schrieffer-Heeger (SSH) model, with bond phonons modulating electron tunneling, is a paradigmatic electron-phonon model that hosts an antiferromagnetic order to bond order transition at half-filling. In the presence of a repulsive Hubbard interaction, the antiferromagnetic phase is enhanced, but the phase transition remains first order. Here, we explore the physics of the SSH model with an attractive Hubbard interaction, which hosts an interesting interplay among charge order, sss-wave pairing, and bond order. Using the numerically exact determinant quantum Monte Carlo method, we show that both charge order, present at weak electron-phonon coupling, and bond order, at large coupling, give way to sss-wave pairing when the system is doped. Furthermore, we demonstrate that the SSH electron-phonon interaction competes with the attractive Hubbard interaction and reduces the sss-wave pairing correlation.
We investigate the two-dimensional optical Su-Schrieffer-Heeger (SSH) model, in which the electron hopping amplitude is modulated by the difference between neighboring phonon coordinates. Using sign-problem-free auxiliary-field quantum Monte Carlo simulations, complemented by mean-field analysis, we determine the long-range ordered phases as a function of the electron-phonon coupling and phonon frequency. By examining both adiabatic and antiadiabatic regimes, we reveal the emergence of staggered and armchair valence bond solid (VBS) phases, as well as the O(4) antiferromagnetic phase. In addition, finite-temperature simulations show that the VBS transition occurs at critical temperatures significantly higher than in models with local electron-phonon coupling, consistent with the presence of lighter polarons in the metallic regime. These findings establish the ground-state and finite-temperature phase diagrams of the optical SSH model, which emphasize its similarities and contrasts with other electron-phonon systems.