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Physical review. B, Condensed matter

Electron-phonon coupling in the two-dimensional Hubbard model: A Monte Carlo study

A. Muramatsu, Werner R. Hanke

Published Jul 1, 1988• 10 citations
Publisher

Abstract

On the basis of quantum Monte Carlo simulations we study the influence of "breathing" lattice distortions on the two-dimensional Hubbard model. In the half-filled band case the system remains stable against the formation of a charge-density wave already for intermediate values ($U=4t$) of the electronic interaction. However, the addition of holes allows for a charge-density-wave state. Thus, the structural instability is not driven by nesting of the Fermi surface, but by the combined effect of doping and Coulomb correlation. The influence of the distortion on the various pairing correlation functions is calculated.

DOI
10.1103/physrevb.38.878

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On the basis of quantum Monte Carlo simulations we study the influence of "breathing" lattice distortions on the two-dimensional Hubbard model. In the half-filled band case the system remains stable against the formation of a charge-density wave already for intermediate values (U=4tU=4tU=4t) of the electronic interaction. However, the addition of holes allows for a charge-density-wave state. Thus, the structural instability is not driven by nesting of the Fermi surface, but by the combined effect of doping and Coulomb correlation. The influence of the distortion on the various pairing correlation functions is calculated.
We present quantum Monte Carlo results for a two-dimensional electron-phonon model. At half filling, a Peierls--charge-density-wave (CDW) instability dominates the behavior of the system and suppresses superconductivity. The CDW structure factor scales with system size and is consistent with a finite-size Ising-like scaling analysis which we use to estimate Tc{\mathit{T}}_{\mathit{c}}Tc​ for the Peierls-CDW transition. Away from half filling, the Monte Carlo calculations show superconducting pairing in an s-wave channel, with a peak in the pair field susceptibility near a region in which there are strong Peierls-CDW correlations.
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Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of sss-wave pairing between charge and magnetic orders
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal) sss-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.
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Quantum Monte Carlo is used to calculate various pairing correlations of the 2D Hubbard model possessing band features experimentally observed in the cuprates. In the hole-doped case, where the Fermi level lies close to the van Hove singularities around (0,π)(0,π)(0,π), the dx2−y2_{x^2-y^2}x2−y2​ pairing correlation is selectively enhanced, while in the electron-doped case, where the singularities are far below the Fermi level and the Fermi surface runs through (±π/2,±π/2)(\pm π/2,\pm π/2)(±π/2,±π/2), both dx2−y2_{x^2-y^2}x2−y2​ and dxy_{xy}xy​ correlations are enhanced with the latter having a 2×2\sqrt{2}\times \sqrt{2}2​×2​ structure. The two pairing symmetries can mix to result in a nodeless gap.