arXiv:1002.1671 · Physical Review B

Threshold singularities in the one-dimensional Hubbard model

Fabian H. L. Eßler

Published May 25, 2010• 57 citations

Abstract

We consider excitations with the quantum numbers of a hole in the one-dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in the single-particle Green's function for commensurate fillings. We present the analogous results for the Yang-Gaudin model (electron gas with $\ensuremath{\delta}$-function interactions).

DOI: 10.1103/physrevb.81.205120

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arXiv:1002.1671 · Physical Review B

Threshold singularities in the one-dimensional Hubbard model

Fabian H. L. Eßler

Published May 25, 2010• 57 citations

arXiv HTML PDF

Abstract

\ensuremath{\delta}

-function interactions).

DOI: 10.1103/physrevb.81.205120

Related papers

Excitation spectrum of the one-dimensional Hubbard model

Cornelius F. Coll

We have extended calculations of the zero-temperature excitation spectrum of the one-dimensional Hubbard model to the case where the number of electrons is less than the number of sites in the chain. The results are computed as a function of the ratio $\frac{U}{t}$ , where $U$ represents the on-site Coulomb repulsion and $t$ is the transfer integral, assumed to be nonzero only for nearest neighbors. Exact calculations are made for the energy and momentum of excitations having single-particle character. Unlike the situation for the half-filled band, we find no gap in the excitation spectrum. We have also considered excitations of the spin-wave type. These are shown to vary linearly with momentum for small momentum. The group velocity for small momentum is found to be inversely proportional to the magnetic susceptibility.We have extended calculations of the zero-temperature excitation spectrum of the one-dimensional Hubbard model to the case where the number of electrons is less than the number of sites in the chain. The results are computed as a function of the ratio $\frac{U}{t}$, where $U$ represents the on-site Coulomb repulsion and $t$ is the transfer integral, assumed to be nonzero only for nearest neighbors. Exact calculations are made for the energy and momentum of excitations having single-particle character. Unlike the situation for the half-filled band, we find no gap in the excitation spectrum. We have also considered excitations of the spin-wave type. These are shown to vary linearly with momentum for small momentum. The group velocity for small momentum is found to be inversely proportional to the magnetic susceptibility.

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Jan 1, 19980 citations

\ensuremath{\delta}

-function interactions).

\frac{U}{t}

, where

U

represents the on-site Coulomb repulsion and

t

is the transfer integral, assumed to be nonzero only for nearest neighbors. Exact calculations are made for the energy and momentum of excitations having single-particle character. Unlike the situation for the half-filled band, we find no gap in the excitation spectrum. We have also considered excitations of the spin-wave type. These are shown to vary linearly with momentum for small momentum. The group velocity for small momentum is found to be inversely proportional to the magnetic susceptibility.

Fixed-node Green's-function Monte Carlo calculations have been performed for very large 16\ifmmode\times\else\texttimes\fi{}16 two-dimensional Hubbard lattices, large interaction strengths

U=10,20,

and

40

, and many $(15\ensuremath{\sim}20)$ densities between empty and half-filling. The nodes were fixed by a simple Slater-Gutzwiller trial wave function. For each value of U we obtained a sequence of ground-state energies which is consistent with the possibility of a phase separation close to half-filling, with a hole density in the hole-rich phase which is a decreasing function of

U

. The energies suffer, however, from a fixed-node bias: more accurate nodes are needed to confirm this picture. Our extensive numerical results and their test against size, shell, shape, and boundary-condition effects also suggest that phase separation is quite a delicate issue, on which simulations based on smaller lattices than considered here are unlikely to give reliable predictions.