Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential

Abstract

The Holstein Hamiltonian describes itinerant electrons whose site density couples to local phonon degrees of freedom. In the single site limit, at half-filling, the electron-phonon coupling results in a double well structure for the lattice displacement, favoring empty or doubly occupied sites. In two dimensions, and on a bipartite lattice in $d\ge 2$, an intersite hopping causes these doubly occupied and empty sites to alternate in a charge density wave (CDW) pattern when the temperature is lowered. Because a discrete symmetry is broken, this occurs in a conventional second-order transition at finite $T_{\mathrm{cdw}}$. In this paper, we investigate the effect of changing the phonon potential energy to one with an intrinsic double well structure even in the absence of an electron-phonon coupling. While this aids in the initial process of pair formation, the implications for subsequent CDW order are non-trivial. One expects that, when the electron-phonon coupling is too strong, the double wells become deep and the polaron mass large, an effect which reduces $T_{\mathrm{cdw}}$. We show here the existence of regions of parameter space where the double well potential, while aiding local pair formation, does so in a way which also substantially enhances long range CDW order.

References in corpus (41)

• The Holstein Polaron
• Continuous-Time Quantum Monte Carlo Algorithm for the Lattice Polaron
• Dimensionality effects on the Holstein polaron
• Two-dimensional Hubbard-Holstein bipolaron
• Quantum Monte Carlo and variational approaches to the Holstein model
• Light Bipolarons Stabilized by Peierls Electron-Phonon Coupling
• Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons
• Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model
• Bipolaronic high-temperature superconductivity
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
• Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
• Competition among Superconducting, Antiferromagnetic, and Charge Orders with Intervention by Phase Separation in the 2D Holstein-Hubbard Model
• Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
• Superconductivity and charge density wave order in the 2D Holstein model
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• A bound on superconducting $T_c$'s
• Langevin Simulations of a Long Range Electron Phonon Model
• Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice
• The anharmonic electron-phonon problem
• Antiferromagnetism induced by electron-phonon-coupling
• Effect of electron-phonon interaction range on lattice polaron dynamics: a continuous-time quantum Monte Carlo study
• Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron
• Electronic inhomogeneity in a Kondo lattice
• Superconductivity, Charge-Density-Waves, and Bipolarons in the Holstein model
• Dominant charge-density-wave correlations in the Holstein model on the half-filled square lattice
• Effects of dimensionality and anisotropy on the Holstein polaron
• Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
• Electron-Phonon Interactions in Flat Band Systems
• Langevin Simulations of the Half-Filled Cubic Holstein Model
• Going beyond the linear approximation in describing electron- phonon coupling: relevance for the Holstein model
• Properties of the non-linear Holstein polaron at finite doping and temperature
• A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in BaBiO${}_3$
• Quantum phonons and the charge density wave transition temperature: a dynamical mean field study
• Charge Density Waves on a Half-Filled Decorated Honeycomb Lattice
• The effects of non-linear electron-phonon interactions on superconductivity and charge-density-wave correlations
• The two-dimensional $t$-$t^{\prime }$ Holstein model
• Quantum Monte Carlo study of an anharmonic Holstein model
• Heavy-Electron Formation and Bipolaronic Transition in the Anharmonic Holstein Model
• Charge Singlets and Orbital-Selective Charge Density Wave Transitions
• Reducing autocorrelation time in determinant quantum Monte Carlo using Wang-Landau algorithm: application to Holstein model

Cited by in corpus (3)

• Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model