a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.

Mark Timothy Cowan

Published Jan 1, 1993• 0 citations

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a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.

Mark Timothy Cowan

Published Jan 1, 1993• 0 citations

OpenAlex

Related papers

Renormalization group computation of correlation functions and particle densities

Pierre Gosselin, Hervé Mohrbach

arXiv:quant-ph/0004103Physics Letters AMay 1, 20012 citations

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

J. W. Bray, S. T. Chui

We calculate $2{k}_{F}$ and $4{k}_{F}$ 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 $\frac{U}{t}=2,10,50$ 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 $4{k}_{F}$ instability arises at very large $U$ and that the $2{k}_{F}$ SDW and $4{k}_{F}$ CDW dominate at large $U$ .We calculate $2{k}_{F}$ and $4{k}_{F}$ 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 $\frac{U}{t}=2,10,50$ 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 $4{k}_{F}$ instability arises at very large $U$ and that the $2{k}_{F}$ SDW and $4{k}_{F}$ CDW dominate at large $U$.

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We have studied correlation functions of the one-dimensional Hubbard model using the density-matrix numerical renormalization-group approach. The singularity exponents of the momentum distribution at k= ${\mathit{k}}_{\mathit{F}}$ and 3 ${\mathit{k}}_{\mathit{F}}$ , as well as the power-law singularity of the spin-correlation function, are computed for large U (U/t= ${10}^{3}$ ). The momentum-distribution exponent at k= ${\mathit{k}}_{\mathit{F}}$ and the spin-correlation exponent are in agreement with the analytic results, while the calculated exponent for momentum distribution at k=3 ${\mathit{k}}_{\mathit{F}}$ is about 3/4, which disagrees with the analytically predicted value 9/8. We also discuss several techniques for an accurate calculation of the correlation functions.We have studied correlation functions of the one-dimensional Hubbard model using the density-matrix numerical renormalization-group approach. The singularity exponents of the momentum distribution at k=${\mathit{k}}_{\mathit{F}}$ and 3${\mathit{k}}_{\mathit{F}}$, as well as the power-law singularity of the spin-correlation function, are computed for large U (U/t=${10}^{3}$). The momentum-distribution exponent at k=${\mathit{k}}_{\mathit{F}}$ and the spin-correlation exponent are in agreement with the analytic results, while the calculated exponent for momentum distribution at k=3${\mathit{k}}_{\mathit{F}}$ is about 3/4, which disagrees with the analytically predicted value 9/8. We also discuss several techniques for an accurate calculation of the correlation functions.

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The phase diagram of the two-leg $t\text{\ensuremath{-}}{J}_{z}$ ladder is explored, using the density-matrix renormalization group method. Results are obtained for energy gaps, electron density profiles, and correlation functions for the half filled and quarter filled cases. The effective Lagrangian velocity parameter ${v}_{\ensuremath{\rho}}$ is shown to vanish at half filling. The behavior of the one-hole gap in the Nagaoka limit is investigated, and found to disagree with theoretical predictions. A tentative phase diagram is presented, which is quite similar to the full $t\text{\ensuremath{-}}J$ ladder, but scaled up by a factor of about 2 in coupling. Near half filling a Luther-Emery phase is found, which may be expected to show superconducting correlations, while near quarter filling the system appears to be in a Tomonaga-Luttinger phase.The phase diagram of the two-leg $t\text{\ensuremath{-}}{J}_{z}$ ladder is explored, using the density-matrix renormalization group method. Results are obtained for energy gaps, electron density profiles, and correlation functions for the half filled and quarter filled cases. The effective Lagrangian velocity parameter ${v}_{\ensuremath{\rho}}$ is shown to vanish at half filling. The behavior of the one-hole gap in the Nagaoka limit is investigated, and found to disagree with theoretical predictions. A tentative phase diagram is presented, which is quite similar to the full $t\text{\ensuremath{-}}J$ ladder, but scaled up by a factor of about 2 in coupling. Near half filling a Luther-Emery phase is found, which may be expected to show superconducting correlations, while near quarter filling the system appears to be in a Tomonaga-Luttinger phase.

arXiv:cond-mat/0511528Physical Review BApr 10, 20061 citation

We calculate

2{k}_{F}

and

4{k}_{F}

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

\frac{U}{t}=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

4{k}_{F}

instability arises at very large

U

and that the

2{k}_{F}

SDW and

4{k}_{F}

CDW dominate at large

U

{\mathit{k}}_{\mathit{F}}

and 3

{\mathit{k}}_{\mathit{F}}

, as well as the power-law singularity of the spin-correlation function, are computed for large U (U/t=

{10}^{3}

). The momentum-distribution exponent at k=

{\mathit{k}}_{\mathit{F}}

and the spin-correlation exponent are in agreement with the analytic results, while the calculated exponent for momentum distribution at k=3

{\mathit{k}}_{\mathit{F}}

is about 3/4, which disagrees with the analytically predicted value 9/8. We also discuss several techniques for an accurate calculation of the correlation functions.