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Physica Scripta

Numerical simulations: some results for the 2- and 3-D Hubbard models and a 2-D electron phonon model

Douglas J. Scalapino, Robert L. Sugar, Steven R. White, N. E. Bickers, Richard T. Scalettar

Published Jan 1, 1989• 4 citations
Publisher

Abstract

Numerical simulations on the half-filled 3-D Hubbard model clearly show the onset of Néel order. Simulations of the 2-D electron-phonon Holstein model show the competition between the formation of a Peierls-CDW state and a superconducting state. However, the behavior of the partly filled 2-D Hubbard model is more difficult to determine. At half-filling, the anti-ferromagnetic correlations grow as T is reduced. Doping away from half-filling supresses these correlations, and we find that there is a weak attractive pairing interaction in the d -wave channel. However, the strength of the pair field susceptibility is weak at the temperatures and lattice sizes we have simulated, and the nature of the low-temperature state of the nearly half-filled Hubbard model remains open.

DOI
10.1088/0031-8949/1989/t27/017

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We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.
The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electron-phonon interactions. In one dimension at half filling, the Holstein electron-phonon coupling promotes on-site pairs of electrons and a Peierls charge-density wave, while the Hubbard on-site Coulomb repulsion UUU promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that (i) as the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions, the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-UUU Hubbard model. (ii) The transitions between Mott/intermediate and intermediate/Peierls states are of the Kosterlitz-Thouless form. (iii) For larger UUU, the two transitions merge at a tricritical point into a single first-order Mott/Peierls transition. In addition, we show that an intermediate phase also occurs in the quarter-filled model.
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.
We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.
Abstract The electron–electron and electron–phonon interactions play an important role in correlated materials, being key features for spin, charge and pair correlations. Thus, here we investigate their effects 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, favouring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.