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Physical review. B, Solid state

Low-temperature properties of the one-dimensional polaron band. I. Extreme-band-narrowing regime

G. Beni, Philip A. Pincus, Junjiro Kanamori

Published Sep 1, 1974• 60 citations
Publisher

Abstract

We consider a narrow one-dimensional tight-binding chain with intra-atomic Coulomb repulsions described in the Hubbard model. The electrons at each site are furthermore assumed to be coupled to a high-frequency local oscillator. In the limit where the oscillator frequency is large compared to the bandwidth, and in the extreme-band-narrowing regime, for various electron densities, we find that: the half-filled-band ground state is an antiferromagnetic insulator; the one-third-filled-band ground state is a diamagnetic insulator; and the one-quarter-filled-band ground state is a weakly coupled system of bound singlet pairs somewhat reminiscent of superconductivity.

DOI
10.1103/physrevb.10.1896

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We consider a narrow one-dimensional tight-binding chain with intra-atomic Coulomb repulsions described in the Hubbard model. The electrons at each site are furthermore assumed to be coupled to a high-frequency local oscillator. In the limit where the oscillator frequency is large compared to the bandwidth, and in the extreme-band-narrowing regime, for various electron densities, we find that: the half-filled-band ground state is an antiferromagnetic insulator; the one-third-filled-band ground state is a diamagnetic insulator; and the one-quarter-filled-band ground state is a weakly coupled system of bound singlet pairs somewhat reminiscent of superconductivity.
A theory of absorption is presented for a half-filled Hubbard band with nearest-neighbour electron transfer (t) and strong intra-site Coulomb repulsion (U). The lineshape is calculated at low temperature (i.e. k B T<<U) to lowest order in t/U for antiferromagnetic, random and ferromagnetic spin configurations in a Cayley tree lattice with a particular emphasis on one dimension. The authors find that the absorption diverges logarithmically at the centre of the absorption band (i.e. at h(cross) omega =U). In a one-dimensional lattice, the absorption width equals twice the bandwidth of a single hole (or an extra electron) in an otherwise half-filled Hubbard band.
We study antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model at low temperature. Collective spin fluctuations are governed by a non-linear sigma model that we derive from the Hubbard model for any value of the Coulomb repulsion. As the Coulomb repulsion increases, the ground state progressively evolves from a Slater to a Mott-Heisenberg antiferromagnet. At finite temperature, we find a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling.
We have investigated the intraband absorption in a single-band Hubbard model at a low concentration ccc (ccc is unity for a filled band) of electrons with a particular emphasis on one-dimensional nearest-neighbor electron transfer. Using a two-particle approximation, we find, for the latter in the frequency range $c\ensuremath{\ll}\ensuremath{\hbar}\ensuremath{\omega}$ (the bandwidth is unity) that the absorption is independent of frequency and vanishes as ${U}^{\ensuremath{-}2}$ for a large on-site Coulomb repulsion UUU. The absorption occurs when an electron is accelerated by another electron in the presence of an oscillating field (i.e., inverse bremsstrahlung). The transport relaxation rate is given by ${\ensuremath{\tau}}^{\ensuremath{-}1}\ensuremath{\propto}c{\ensuremath{\omega}}^{2}{U}^{\ensuremath{-}2}$. In the limit $U=\ensuremath{\infty}$ the present result supports the spinless fermion model, according to which the intraband absorption vanished for $\ensuremath{\omega}\ensuremath{\ne}0$. In the presence of second-nearest-neighbor electron transfer (t2{t}_{2}t2​) such that $c\ensuremath{\ll}|{t}_{2}|$, the ${\ensuremath{\omega}}^{\ensuremath{-}2}$-frequency dependence of the absorption obtains as in two or three dimensions.
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.
Correlation effects in the one-dimensional Hubbard model are studied by application of the L-resolvent method. The calculations are well beyond one-particle mean field approximation. All correlations involving two neighboring sites are included exactly and higher order correlations are approximated. The effects of varying temperature, band filling, Coulomb repulsion and external magnetic field are investigated. Two-site correlations for non-half-filled band fillings are calculated for the first time. Some exact relations between correlation functions are derived by electron-hole symmetry. Results indicate that short-range spin correlations always favor antiferromagnetic order. Large Coulomb repulsion induces a gap in the excitation spectrum and a metal-insulator transition is predicted as the Coulomb repulsion parameter is changed.