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arXiv:cond-mat/0002031 · Physical review. B, Condensed matter

Charge-density waves in the Hubbard chain: Evidence for 4kF instability

Thereza Paiva, Raimundo R. dos Santos

Published May 15, 2000• 7 citations
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Abstract

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 ${4k}_{F}$ instability dominating over the ${2k}_{F}$ 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 ${2k}_{F}$ contribution vanishes above some ${U}^{*}(\ensuremath{\rho}).$

DOI
10.1103/physrevb.61.13480

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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 \ensuremathρ=1/6\ensuremath{\rho}=1/6\ensuremathρ=1/6 and 1/3; for \ensuremathρ=1/2\ensuremath{\rho}=1/2\ensuremathρ=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∗(\ensuremathρ).{U}^{*}(\ensuremath{\rho}).U∗(\ensuremathρ).
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.
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.
We used exact diagonalization of small clusters and exact results in various limits to determine the phase diagram and the critical exponents of the one-dimensional (1D) U-V model at quarter-filling. We found an instability of the Luttinger liquid to a charge density wave (CDW) insulator across a boundary going from ( U, V ) = (+ ∞ , 2 t ) to (4 t , + ∞ ). In the metallic phase, the dominant fluctuations are superconducting if V is large enough and spin density wave (SDW) otherwise. In the latter case, the critical exponent α of the momentum distribution does not exceed 9/16. The relevance of these results to 1D organic conductors is discussed.
We study the formation of charge density waves (CDW's) in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive (U>0)(U>0)(U>0) and free (U=0)(U=0)(U=0) sites. By means of Lanczos diagonalizations for the ground state, we calculate the charge structure factor. Our results show that while the superlattice structure affects the modulation of the charge density waves, the periodicity can still be predicted through an effective density. We also show that, for a fixed repulsive layer thickness, the periodicity of the CDW is an oscillatory function of the free layer thickness.
We find and characterize the instabilities of the repulsive Hubbard chain in a magnetic field by studying all response functions at low frequency \ensuremath{\omega} and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) \ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow} Fermi points, \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$. For finite values of the on-site repulsion U the instabilities occur for single \ensuremath{\sigma} electron added or removed at momenta \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$, for transverse spin-density wave (SDW) at momenta \ifmmode\pm\else\textpm\fi{}2kF{2\mathrm{k}}_{\mathrm{F}}2kF​ (where 2kF{2\mathrm{k}}_{\mathrm{F}}2kF​=${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$), and for a charge-density wave and SDW at momenta \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$ and \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$. While removing or adding single electrons is dominant at zero magnetic field, the presence of that field brings about a dominance for the transverse \ifmmode\pm\else\textpm\fi{}2kF{2\mathrm{k}}_{\mathrm{F}}2kF​ SDW over all the remaining instabilities for a large domain of U and density n values. We go beyond conformal-field theory and study divergences which occur at finite frequency in the one-electron Green function at half-filling and in the transverse-spin response function in the fully polarized ferromagnetic phase.
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.