World-line Quantum Monte Carlo Simulation of the Hubbard-Holstein Model

Quantum Monte Carlo (QMC) method is a powerful tool to understand the physics of strongly correlated interacting quantum system. Persistent questions concerning the role of phonons in strongly correlated materials like manganites, cuprates, iron pnictides, and organic superconductors keep the study of electron-phonon Hamiltonians at the forefront of research. We use world-line quantum Monte Carlo (WLQMC) to explore the ground state and finite temperature properties of one-dimensional many-body systems based on the extended Hubbard-Holstein Hamiltonian. This method is based on a direct-space, imaginary-time representation of the fermion and boson fields, which allows us to describe the regimes with dominant charge-density-wave, superconductivity and metallic behavior. We show the ground state and finite temperature phase diagrams of the Hubbard-Holstein model as a function of Hubbard U, nearest neighbor interaction V, phonon frequency ω and electron-phonon coupling constant λ. We show the simulation results for an extension of the Hamiltonian to a situation where electron-phonon interaction is long range.