Physical Review Letters

2pF and 4pF Instabilities in the One-Dimensional Electron Gas

J. E. Hirsch, Douglas J. Scalapino

Published Apr 11, 1983• 50 citations

Abstract

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 $2{p}_{\mathrm{F}}$ charge-density singularity, while they enhance the $2{p}_{\mathrm{F}}$ spin-density singularity. The $4{p}_{\mathrm{F}}$ 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.

DOI: 10.1103/physrevlett.50.1168

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Physical Review Letters

2pF and 4pF Instabilities in the One-Dimensional Electron Gas

J. E. Hirsch, Douglas J. Scalapino

Published Apr 11, 1983• 50 citations

Publisher

Abstract

2{p}_{\mathrm{F}}

charge-density singularity, while they enhance the

2{p}_{\mathrm{F}}

spin-density singularity. The

4{p}_{\mathrm{F}}

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.

DOI: 10.1103/physrevlett.50.1168

Related papers

2pF and 4pF instabilities in a one-quarter-filled-band Hubbard model

J. E. Hirsch, Douglas J. Scalapino

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 $2{p}_{F}$ charge-density response and enhance the $2{p}_{F}$ spin-density response. While a strictly on-site Coulomb interaction gives rise to only a weak $4{p}_{F}$ structure in the charge-density response, longer-range Coulomb interactions such as the near-neighbor interaction $V$ in the extended Hubbard model can produce a singularity at $4{p}_{F}$ . 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.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 $2{p}_{F}$ charge-density response and enhance the $2{p}_{F}$ spin-density response. While a strictly on-site Coulomb interaction gives rise to only a weak $4{p}_{F}$ structure in the charge-density response, longer-range Coulomb interactions such as the near-neighbor interaction $V$ in the extended Hubbard model can produce a singularity at $4{p}_{F}$. 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.

Physical review. B, Condensed matterJun 15, 1983129 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

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.

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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

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 $U$.

Physical review. B, Condensed matterMay 15, 197953 citations

Charge Gap in One-Dimensional Extended Hubbard Model

Guo-Hui Ding, Fei Ye, Xu Bo-wei

Communications in Theoretical PhysicsJan 15, 20033 citations

2{p}_{\mathrm{F}}

charge-density singularity, while they enhance the

2{p}_{\mathrm{F}}

spin-density singularity. The

4{p}_{\mathrm{F}}

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.

2{p}_{F}

charge-density response and enhance the

2{p}_{F}

spin-density response. While a strictly on-site Coulomb interaction gives rise to only a weak

4{p}_{F}

structure in the charge-density response, longer-range Coulomb interactions such as the near-neighbor interaction

V

in the extended Hubbard model can produce a singularity at

4{p}_{F}

. 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.

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 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 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