Charge-Density Wave Order on a $\pi$-flux Square Lattice

Abstract

The effect of electron-phonon coupling (EPC) on Dirac fermions has recently been explored numerically on a honeycomb lattice, leading to precise quantitative values for the finite temperature and quantum critical points. In this paper, 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 honeycomb lattice geometry, presenting results for a range of phonon frequencies $0.1⩽\omega ⩽2.0$. We find that the interactions give rise to charge-density wave (CDW) order, but only above a finite coupling strength ${\lambda }_{\mathrm{crit}}$. The transition temperature is evaluated and presented in a $T_c$-$\lambda$ phase diagram. An accompanying mean-field theory (MFT) calculation also predicts the existence of quantum phase transition (QPT), but at a substantially smaller coupling strength.

arXiv comment9 pages, 13 figures

References in corpus (29)

• The electronic properties of graphene
• Graphene: Status and Prospects
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• The Flux-Phase of the Half-Filled Band
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron
• Dimensionality effects on the Holstein polaron
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Two-dimensional Hubbard-Holstein bipolaron
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions
• Metal-insulator transition in the one-dimensional Holstein model at half filling
• Quantum Monte Carlo and variational approaches to the Holstein model
• Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Effect of electron-phonon interaction range on lattice polaron dynamics: a continuous-time quantum Monte Carlo study
• Quantum disordered phase near the Mott transition in the staggered-flux Hubbard model on a square lattice
• Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron
• Effects of dimensionality and anisotropy on the Holstein polaron
• Interaction effect in two-dimensional Dirac fermions
• Mott transition in the $\pi$-flux SU($4$) Hubbard model on a square lattice
• Charge Density Waves on a Half-Filled Decorated Honeycomb Lattice
• Mott Transition in the Two-Dimensional Flux Phase
• Quantum phase transitions of multi-species Dirac fermions
• Exotic pairing symmetry of interacting Dirac fermions on a $\pi$ flux lattice
• Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points
• Strongly fluctuating fermionic superfluid in attractive π-flux Hubbard model

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• Quantum phase transitions in Dirac fermion systems
• Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study
• Magnetism and charge order in the honeycomb lattice
• Triplet Pair-Density Wave Superconductivity on the $\pi$-flux Square Lattice
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Anomalous Floquet Phases. A resonance phenomena
• Charge Singlets and Orbital-Selective Charge Density Wave Transitions
• Pseudo-magnetic fields in square lattices
• Low-energy effective theory and symmetry classification of flux phases on Kagome lattice
• The competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction