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Physical review. B, Condensed matter

2pF and 4pF instabilities in a one-quarter-filled-band Hubbard model

J. E. Hirsch, Douglas J. Scalapino

Published Jun 15, 1983• 129 citations
Publisher

Abstract

The zero-frequency wave-vector-dependent charge- and spin-density susceptibilities for a quarter-filled-band extended Hubbard model are calculated with the use of a Monte Carlo technique. Results for a variety of different temperatures are given. Coulomb interactions are found to suppress the $2{p}_{F}$ charge-density response and enhance the $2{p}_{F}$ spin-density response. While a strictly on-site Coulomb interaction gives rise to only a weak $4{p}_{F}$ structure in the charge-density response, longer-range Coulomb interactions such as the near-neighbor interaction $V$ in the extended Hubbard model can produce a singularity at $4{p}_{F}$. In addition to these susceptibilities, both the charge and spin structure factors are calculated, as well as two-particle, two-hole correlation functions. We also show some results for the ground-state energy, magnetic susceptibility, and specific heat of the Hubbard model. The relationship of the results obtained from our Monte Carlo simulations to various limiting exact results as well as to the well-known weak coupling renormalization-group predictions are discussed.

DOI
10.1103/physrevb.27.7169

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The zero-frequency wave-vector-dependent charge- and spin-density susceptibilities for a quarter-filled-band extended Hubbard model are calculated with the use of a Monte Carlo technique. Results for a variety of different temperatures are given. Coulomb interactions are found to suppress the 2pF2{p}_{F}2pF​ charge-density response and enhance the 2pF2{p}_{F}2pF​ spin-density response. While a strictly on-site Coulomb interaction gives rise to only a weak 4pF4{p}_{F}4pF​ structure in the charge-density response, longer-range Coulomb interactions such as the near-neighbor interaction VVV in the extended Hubbard model can produce a singularity at 4pF4{p}_{F}4pF​. In addition to these susceptibilities, both the charge and spin structure factors are calculated, as well as two-particle, two-hole correlation functions. We also show some results for the ground-state energy, magnetic susceptibility, and specific heat of the Hubbard model. The relationship of the results obtained from our Monte Carlo simulations to various limiting exact results as well as to the well-known weak coupling renormalization-group predictions are discussed.
Charge- and spin-density response functions in the one-dimensional \textonequarter{}-filled extended Hubbard model have been studied by use of a Monte Carlo technique. The results show that Coulomb interactions suppress the 2pF2{p}_{\mathrm{F}}2pF​ charge-density singularity, while they enhance the 2pF2{p}_{\mathrm{F}}2pF​ spin-density singularity. The 4pF4{p}_{\mathrm{F}}4pF​ response is only appreciable if, in addition to on-site repulsion, longer-range interactions exist. The present results are compared with weak-coupling renormalization-group predictions.
We continue our study of correlation functions in the one-dimensional Hubbard model with the use of a Monte Carlo technique. This paper focuses on the behavior of two different particle-hole susceptibilities: the on-site charge-density response function and the nearest-neighbor charge-transfer response function. Although their behavior is predicted to be similar within weak-coupling renormalization-group theory, we find different behavior with our nonperturbative technique. In particular, the charge-transfer susceptibility shows structure at 2pF2{p}_{F}2pF​ for large Coulomb interactions due to spin-Peierls fluctuations, which is absent in the on-site charge-density response. We also study the effect of varying band filling, by comparing results for the 14\frac{1}{4}41​- filled band ($\ensuremath{\rho}=0.5$) case and the cases $\ensuremath{\rho}=0.61$ and $\ensuremath{\rho}=1$. We find, for example, that it is possible to have structure in the response function at wave vectors that are not simply related to the Fermi wave vector. We discuss the implications of our results to the interpretation of experimental results in various quasi-one-dimensional charge-transfer compounds.
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.
Charge-density waves in the Hubbard chain are studied by means of finite-temperature quantum Monte Carlo simulations and Lanczos diagonalizations for the ground state. We present results both for the charge susceptibilities and for the charge structure factor at densities $\ensuremath{\rho}=1/6$ and 1/3; for $\ensuremath{\rho}=1/2$ (quarter filled) we only present results for the charge structure factor. The data are consistent with a 4kF{4k}_{F}4kF​ instability dominating over the 2kF{2k}_{F}2kF​ one, at least for sufficiently large values of the Coulomb repulsion U. This can only be reconciled with the Luttinger liquid analyses if the amplitude of the 2kF{2k}_{F}2kF​ contribution vanishes above some ${U}^{*}(\ensuremath{\rho}).$
We analyze the charge fluctuations in the two-dimensional quarter-filled extended Hubbard model on an anisotropic triangular lattice. We formulate the patch functional-renormalization-group method for this system and examine the full momentum dependence of the charge/spin susceptibilities. Two distinct peak structures in the charge susceptibility are obtained, where one is due to the Fermi-surface nesting condition and the other is due to the intersite Coulomb repulsions. It is shown that the mode-coupling effects within the particle-hole channel are crucial to improve the results of the random-phase-approximation, while the mode-coupling effects involving the particle-particle channel do not have strong effects. The validity of the random-phase-approximation is also discussed.
We extend previous calculations of the 2kF2{k}_{F}2kF​ and 4kF4{k}_{F}4kF​ (${k}_{F}\ensuremath{\equiv}\mathrm{Fermi}\mathrm{wave}\mathrm{vector}$) spin- and charge-density autocorrelation functions of the one-dimensional Hubbard model by including the nearest-neighbor Coulomb interaction VVV. The results are computed for finite chains containing up to eight sites using a computer renormalization-group technique previously developed by us. We find, inter alia, that the real part of the 4kF4{k}_{F}4kF​ charge-density wave (CDW), which is comparable to the real part of the 2kF2{k}_{F}2kF​ CDW when only large onsite Coulomb repulsion is considered, becomes greatly enhanced relative to the 2kF2{k}_{F}2kF​ CDW when VVV is positive. This finding implies that the VVV interaction is important in explaining the 4kF4{k}_{F}4kF​ instability of some quasi-one-dimensional materials.