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arXiv:2407.09366 · Physical review. B./Physical review. B

Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger model and its relevance to graphene

Sohan Malkaruge Costa, Benjamin Cohen-Stead, Steven Johnston

Published Sep 16, 2024• 5 citations
arXivHTMLPDF

Abstract

We perform sign-problem-free determinant quantum Monte Carlo simulations of the optical Su-Schrieffer-Heeger model on a half-filled honeycomb lattice. In particular, we investigate the model's semimetal (SM) to Kekul\'e valence bond solid (KVBS) phase transition at zero and finite temperatures as a function of phonon energy and interaction strength. Using hybrid Monte Carlo sampling methods, we can simulate the model near the adiabatic regime, allowing us to access regions of parameter space relevant to graphene. Our simulations suggest that the SM-KVBS transition is weakly first-order at all temperatures, with graphene situated close to the phase boundary in the SM region of the phase diagram. Our results highlight the important role bond-stretching phonon modes play in the formation of KVBS order in strained graphene-derived systems.

DOI
10.1103/physrevb.110.115130

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We perform sign-problem-free determinant quantum Monte Carlo simulations of the optical Su-Schrieffer-Heeger model on a half-filled honeycomb lattice. In particular, we investigate the model's semimetal (SM) to Kekul'e valence bond solid (KVBS) phase transition at zero and finite temperatures as a function of phonon energy and interaction strength. Using hybrid Monte Carlo sampling methods, we can simulate the model near the adiabatic regime, allowing us to access regions of parameter space relevant to graphene. Our simulations suggest that the SM-KVBS transition is weakly first-order at all temperatures, with graphene situated close to the phase boundary in the SM region of the phase diagram. Our results highlight the important role bond-stretching phonon modes play in the formation of KVBS order in strained graphene-derived systems.
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.
Motivated by recent experimental findings of correlating insulator and superconductor behavior in twisted bilayer graphene, the authors study a cluster charge interaction model on a honeycomb lattice. The cluster charge is defined on the dual lattice of honeycomb to mimic charge centers forming a triangular lattice found in experiments. Based on unbiased sign-problem-free quantum Monte Carlo simulations, the authors determine the phase diagram for this model. It features a fermionic quantum critical point with chiral XY universality and a Kekul\'e valence bond solid phase at intermediate interaction, which may be related to the correlating insulator phase found in experiments. This is an example of the rich phases found in a simple model without artificial design.
We use exact quantum Monte Carlo simulations to demonstrate that the N\'eel ground state of an antiferromagnetic SU(2) spin-12\frac{1}{2}21​ Heisenberg model on the honeycomb lattice can be destroyed by a coupling to quantum phonons. We find a clear first-order transition to a valence bond solid state with Kekul\'e order instead of a deconfined quantum critical point. However, quantum lattice fluctuations can drive the transition towards weakly first order, revealing a tunability of the transition by the retardation of the interaction. In contrast to the one-dimensional case, our phase diagram in the adiabatic regime is qualitatively different from the frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. Our results suggest that a coupling to bond phonons can induce Kekul\'e order in Dirac systems.
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.
Electron-phonon (eee-ph) interactions arise in many strongly correlated quantum materials from the modulation of the nearest-neighbor hopping integrals, as in the celebrated Su-Schrieffer-Heeger (SSH) model. Nevertheless, relatively few non-perturbative studies of correlated SSH models have been conducted in dimensions greater than one, and those that have been done have primarily focused on bond models, where generalized displacements independently modulate each hopping integral. We conducted a sign-problem free determinant quantum Monte Carlo study of the optical SSH-Hubbard model on a two-dimensional square lattice, where site-centered phonon modes simultaneously modulate pairs of nearest-neighbor hopping integrals. We report the model's low-temperature phase diagram in the challenging adiabatic regime (Ω/EF∼1/8Ω/E_\mathrm{F} \sim 1/8Ω/EF​∼1/8). It exhibits insulating antiferromagnetic Mott and bond-order-wave (BOW) phases with a narrow region of coexistence between them. We also find that a critical eee-ph coupling is required to stabilize the BOW phase in the small UUU limit. Lastly, in stark contrast to recent findings for the model's bond variant, we find no evidence for a long-range antiferromagnetism in the pure (U/t=0)(U/t=0)(U/t=0) optical SSH model.
The Hubbard and Su-Schrieffer-Heeger (SSH) Hamiltonians 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 UUU between up and down electrons induces antiferromagnetic (AFM) order and a Mott insulating phase. On the other hand, for the SSH model, there is an AFM phase when the electron-phonon coupling $\ensuremath{\lambda}$ is less than a critical value ${\ensuremath{\lambda}}_{c}$ and a bond order wave when $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}$. In this Letter, we perform numerical studies on the square lattice optical Su-Schrieffer-Heeger-Hubbard Hamiltonian, which combines both interactions. We use the determinant quantum Monte Carlo 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 $\ensuremath{\lambda}$ increases. The AFM phase is characterized by two different regions. At smaller $\ensuremath{\lambda}$ the behavior is similar to that of the pure Hubbard model; the other region, while maintaining long-range AFM order, exhibits larger kinetic energies and double occupancy, i.e., larger quantum fluctuations, similar to the AFM phase found in the pure SSH model.