Effect of Electron-Phonon Interactions in the Holstein Model on a Staggered-Flux Square Lattice*

The effect of electron-phonon coupling on Dirac fermions raises interesting questions concerning charge-density wave (CDW) formation in a semi-metal, which have recently been explored on a honeycomb lattice[1,2]. Here, we use the unbiased determinant Quantum Monte Carlo (DQMC) method to study the Holstein model on a half-filled staggered-flux square lattice, and compare with the results on the honeycomb lattice. Our work analyzes a range of phonon frequencies, 0.1 ≤ ω ≤ 2.0. We find that interactions give rise to charge-density wave order but only above a finite coupling strength λ_crit. The transition temperature is evaluated and presented in a T_c - λ phase diagram. An accompanying mean-field theory (MFT) calculation also reveals the existence of quantum phase transition, although at a smaller critical coupling strength than found in DQMC.

[1] "Charge Order in the Holstein Model on a Honeycomb Lattice," Y.-X. Zhang, W.-T. Chiu, N.C. Costa, G.G. Batrouni, and R.T. Scalettar, Phys. Rev. Lett. 122, 077602 (2019).
[2] "Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons," Chuang Chen, Xiao Yan Xu, Zi Yang Meng, and Martin Hohenadler, Phys. Rev. Lett. 122, 077601 (2019).