Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

Abstract

We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic order at half-filling.

Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

“…Instead, DMFT calculations showed contradictory results, with either a direct transition between CDW and Mott insulators [22] or the presence of a small intermediate phase [23]. Also in two dimensions the situation is not conclusive, since only few calculations have been afforded [31,32], where some evidence for the emergence of an intermediate metallic phase has been suggested at finite temperatures. In addition, away from half filling, the sign problem is so strong that it prevents one from performing any stable simulation.…”

“…The two-dimensional case has been relatively little investigated in the past. Indeed, quantum Monte Carlo techniques suffer from the sign problem and stable simulations can be accomplished only in few cases [30][31][32]. Therefore, the Hubbard-Holstein model has been mainly considered within mean-field approaches [33][34][35][36] or by using perturbative methods [37,38].…”

Variational Monte Carlo method for electron-phonon coupled systems

“…There are several numerical methods to tackle the problems of electron-phonon coupled systems such as the exact diagonalization (ED) [4,5], the density matrix renormalization group (DMRG) [6][7][8][9][10][11][12], the quantum Monte Carlo (QMC) method [13][14][15][16][17][18][19][20][21][22][23], the dynamical mean-field theory (DMFT) [24][25][26][27][28][29], and so on. Although the ED provides exact results, it is limited to finite clusters.…”

Polaronic approach to strongly correlated electron systems with strong electron-phonon interaction

“…Similar competition has been revealed earlier by the Quantum Monte Carlo method. 12 The transformation of the phonon cloud with the maximum at 0-phonon component to the multiphonon maximum for two-hole states (13) with diagonal EPI occurs smoothly in the region λ d = 0.025 − 0.03 (almost the same as for single-hole states (12)), nevertheless the evolution the large local polaron to the small local polaron continues up to λ d = 0.9 (Fig. 4d) In the regime of equal diagonal and off-diagonal EPI up to λ < 0.314 the population of oxygen holes negligibly increases and the copper holes population decreases with strengthening the EPI (Fig.…”

“…The stronger EPI the larger is population of hole on copper orbital that results from the hole self-trapping, because oxygen holes are more mobile than copper ones. Smoothly with λ d growth at λ d = 0.03 − 0.04 the phonon cloud transforms from the narrow distribution with the maximum at 0-phonon component in the eigenstates (12) to the multiphonon components. Nevertheless the partial occupation of oxygen orbital takes place for large EPI also.…”