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Physical review. B, Condensed matter

Computer renormalization-group calculations of the 2kF and 4kF correlation functions of an extended one-dimensional Hubbard model

S. T. Chui, J. W. Bray

Published Feb 15, 1980• 20 citations
Publisher

Abstract

We extend previous calculations of the $2{k}_{F}$ and $4{k}_{F}$ (${k}_{F}\ensuremath{\equiv}\mathrm{Fermi}\mathrm{wave}\mathrm{vector}$) spin- and charge-density autocorrelation functions of the one-dimensional Hubbard model by including the nearest-neighbor Coulomb interaction $V$. 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 $4{k}_{F}$ charge-density wave (CDW), which is comparable to the real part of the $2{k}_{F}$ CDW when only large onsite Coulomb repulsion is considered, becomes greatly enhanced relative to the $2{k}_{F}$ CDW when $V$ is positive. This finding implies that the $V$ interaction is important in explaining the $4{k}_{F}$ instability of some quasi-one-dimensional materials.

DOI
10.1103/physrevb.21.1380

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Computer renormalization-group calculations of 2kF and 4kF correlation functions of the one-dimensional Hubbard model

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Physical review. B, Condensed matter•Jan 1, 1997•40 citations
We extend previous calculations of the 2kF2{k}_{F}2kF​ and 4kF4{k}_{F}4kF​ (kF\ensuremath≡Fermiwavevector{k}_{F}\ensuremath{\equiv}\mathrm{Fermi}\mathrm{wave}\mathrm{vector}kF​\ensuremath≡Fermiwavevector) 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 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.
We study the effects of a bond-charge interaction (or correlated hopping) on the properties of the extended [i.e., with both on-site (U) and nearest-neighbor (V) repulsions] Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, X, the charge-density-wave (CDW) state is more robust than the spin-density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when X=0. For X=t and fixed V2t (t is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponds to a different density of doubly occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any X in the range examined. \textcopyright{} 1996 The American Physical Society.
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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 present a generalization of the recently proposed variational cluster perturbation theory to extended Hubbard models at half-filling with repulsive nearest neighbor interaction. The method takes into account short-range correlations correctly by the exact diagonalization of clusters of finite size, whereas long-range order beyond the size of the clusters is treated on a mean-field level. For one dimension, we show that quantum Monte Carlo and density-matrix renormalization-group results can be reproduced with very good accuracy. Moreover we apply the method to the two-dimensional extended Hubbard model on a square lattice. In contrast to the one-dimensional case, a first order phase transition between spin density wave phase and charge density wave phase is found as function of the nearest-neighbor interaction at onsite interactions $U\ensuremath{\geqslant}3t$. The single-particle spectral function is calculated for both the one-dimensional and the two-dimensional system.
We consider a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and nearest-neighbor hopping for spin \ensuremath{\sigma}, which depends on the sum of particles ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$ with opposite spin in the two sites involved. The hopping matrix elements are denoted by tAA{\mathrm{t}}_{\mathrm{AA}}tAA​,tAB{\mathrm{t}}_{\mathrm{AB}}tAB​,tBB{\mathrm{t}}_{\mathrm{BB}}tBB​ for ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$=0,1,2, respectively. For 0tAB{\mathrm{t}}_{\mathrm{AB}}tAB​tAA{\mathrm{t}}_{\mathrm{AA}}tAA​=tBB{\mathrm{t}}_{\mathrm{BB}}tBB​, we have determined the regions of parameters for which the ground-state (GS) of the one-dimensional system is a charge-density wave (CDW), a spin-density wave (SDW), or a metal (M), using Hartree-Fock, exact diagonalization of finite chains and quantum Monte Carlo. The results agree qualitatively with the exactly solvable limit of tAB{\mathrm{t}}_{\mathrm{AB}}tAB​=0. For 0tAB{\mathrm{t}}_{\mathrm{AB}}tAB​tAA{\mathrm{t}}_{\mathrm{AA}}tAA​=tBB{\mathrm{t}}_{\mathrm{BB}}tBB​, the GS is a M for sufficiently low values of U and V. In contrast, when tAA{\mathrm{t}}_{\mathrm{AA}}tAA​+tBB{\mathrm{t}}_{\mathrm{BB}}tBB​-2tAB{2\mathrm{t}}_{\mathrm{AB}}2tAB​=0, our results suggest that the GS is either a CDW or a SDW, with the boundary between them lying near the line U=2V.