Physical review. B, Condensed matter

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

J. W. Bray, S. T. Chui

Published May 15, 1979• 53 citations

Abstract

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 $U$.

DOI: 10.1103/physrevb.19.4876

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Physical review. B, Condensed matter

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

J. W. Bray, S. T. Chui

Published May 15, 1979• 53 citations

Publisher

Abstract

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

DOI: 10.1103/physrevb.19.4876

Related papers

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

S. T. Chui, J. W. Bray

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.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.

Physical review. B, Condensed matterFeb 15, 198020 citations

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

J. E. Hirsch, Douglas J. Scalapino

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.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.

Physical review. B, Condensed matterMay 15, 1984102 citations

Bond-charge interaction in the extended Hubbard chain

Daisy M. Luz, Raimundo R. dos Santos

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.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.

arXiv:cond-mat/9603164Physical review. B, Condensed matterJul 1, 199610 citations

Phase diagram and correlation functions of the half-filled extended Hubbard model in one dimension

Johannes Voit

The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.

Physical review. B, Condensed matterFeb 15, 1992142 citations

Density-matrix renormalization-group calculation of correlation functions in the one-dimensional Hubbard model

Shaojin Qin, Shoudan Liang, Zhao-Bin Su +1 more

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.

Physical review. B, Condensed matterAug 15, 199530 citations

Quantum coherence and decoherence of correlated electron states in the one-dimensional charge-density-wave–spin-density-wave phase transition

Norikazu Tomita

The charge-density-wave (CDW)--spin-density-wave (SDW) phase transition of the one-dimensional extended Hubbard model is investigated in the strong correlation regime, from the viewpoint of the quantum coherence or decoherence of the two correlated states. In the finite-size system, the CDW wave function, near the phase boundary, has the significant quantum fluctuations due to the SDW domains. The superposition of these SDW domains leads to the quantum coherence between the CDW and SDW wave functions. However, the scaling analysis shows that the density of the SDW fluctuations becomes asymptotically zero in the infinite-size limit, which indicates the decoherence of the two states in the bulk phase transition.The charge-density-wave (CDW)--spin-density-wave (SDW) phase transition of the one-dimensional extended Hubbard model is investigated in the strong correlation regime, from the viewpoint of the quantum coherence or decoherence of the two correlated states. In the finite-size system, the CDW wave function, near the phase boundary, has the significant quantum fluctuations due to the SDW domains. The superposition of these SDW domains leads to the quantum coherence between the CDW and SDW wave functions. However, the scaling analysis shows that the density of the SDW fluctuations becomes asymptotically zero in the infinite-size limit, which indicates the decoherence of the two states in the bulk phase transition.

Physical Review BMar 10, 20063 citations

We calculate

2{k}_{F}

and

4{k}_{F}

\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 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.

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.

{\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.