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Physical review. B, Condensed matter

2pF and 4pF instabilities in the one-dimensional Hubbard model

J. E. Hirsch, Douglas J. Scalapino

Published May 15, 1984• 102 citations
Publisher

Abstract

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 $2{p}_{F}$ 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 $\frac{1}{4}$- 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.

DOI
10.1103/physrevb.29.5554

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Physical review. B, Condensed matter•May 15, 1979•53 citations
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 (\ensuremathρ=0.5\ensuremath{\rho}=0.5\ensuremathρ=0.5) case and the cases \ensuremathρ=0.61\ensuremath{\rho}=0.61\ensuremathρ=0.61 and \ensuremathρ=1\ensuremath{\rho}=1\ensuremathρ=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.
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 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.
We study the spin and charge fluctuations of the extended Hubbard model with on-site interaction UUU and first neighbor interaction VVV on the two-dimensional square lattice in the weak to intermediate coupling regime. We propose an extension of the two-particle self-consistent approximation that includes the effect of functional derivatives of the pair-correlation functions on irreducible spin and charge vertices. These functional derivatives were ignored in our previous work. We evaluate them assuming particle-hole symmetry. The resulting theory satisfies conservation laws and the Mermin-Wagner theorem. Our current results are in much better agreement with benchmark quantum Monte Carlo results. This theory allows us to reliably determine the crossover temperatures toward renormalized-classical regimes, and hence, the dominant instability as a function of UUU and VVV. We have considered fillings n=1n=1n=1 and n=0.75n=0.75n=0.75. Either spin or charge fluctuations can dominate. The wave vector is self-determined by the approach.
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 calculate 2kF2{k}_{F}2kF​ and 4kF4{k}_{F}4kF​ charge-density wave (CDW) and spin-density wave (SDW) autocorrelation functions for the one-dimensional Hubbard model using a computer renormalization-group technique previously developed by us. We describe the method and expected accuracy of the results. The correlation functions are calculated for Hubbard parameter Ut=2,10,50\frac{U}{t}=2,10,50tU​=2,10,50 and for two different band fillings. We obtain, describe, and compare for the first time the magnitudes and temperature dependences of the correlation functions. We find, inter alia, that the 4kF4{k}_{F}4kF​ instability arises at very large UUU and that the 2kF2{k}_{F}2kF​ SDW and 4kF4{k}_{F}4kF​ CDW dominate at large UUU.