JOURNAL OF ADVANCES IN PHYSICS

Momentum Distribution Critical Exponents for 1D Hubbard model in a Magnetic Field

Nelson Oyindenyifa Nenuwe, J. O. A. Idiodi

Published Nov 20, 2015• 0 citations

Abstract

Critical exponents at and for the momentum distribution function are studied for one-dimensional Hubbard model in the presence of magnetic field, using conformal field theory (CFT) approach. Exponents at and are reproduced. Results at is in contrast to earlier numerical prediction of 1, while at , the exponent is 49/8. The singularities at and appears to be weak and gradually degenerating into a smooth curve.

DOI: 10.24297/jap.v11i3.468

Related papers

Momentum-distribution critical exponents for the one-dimensional large-UHubbard model in the thermodynamic limit

Shaojin Qin, Lu Yu

Physical review. B, Condensed matterJul 15, 19967 citations

Tomonaga-Luttinger Liquid Exponents of Correlation Functions around Fermi points in the Hubbard Model

Nelson Oyindenyifa Nenuwe, J. O. A. Idiodi

arXiv:1507.07254Advances in physics theories and applicationsJul 26, 20150 citations

Critical exponents for the one-dimensional Hubbard model

Holger Frahm, V. E. Korepin

Physical review. B, Condensed matterDec 1, 1990502 citations

Tomonaga-Luttinger Unusual Exponents around Fermi Points in the One-Dimensional Hubbard Model

Nelson Oyindenyifa Nenuwe, J. O. A. Idiodi

World Journal of Condensed Matter PhysicsJan 1, 20151 citation

Magnetic-field effects on the correlation functions in the one-dimensional strongly correlated Hubbard model

Masao Ogata, Tadao Sugiyama, Hiroyuki Shiba

Physical review. B, Condensed matterApr 1, 199155 citations

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

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

Physical review. B, Condensed matterAug 15, 199530 citations

JOURNAL OF ADVANCES IN PHYSICS

Momentum Distribution Critical Exponents for 1D Hubbard model in a Magnetic Field

Nelson Oyindenyifa Nenuwe, J. O. A. Idiodi

Published Nov 20, 2015• 0 citations

Publisher

Abstract

DOI: 10.24297/jap.v11i3.468

Related papers

Momentum-distribution critical exponents for the one-dimensional large-UHubbard model in the thermodynamic limit

Shaojin Qin, Lu Yu

The critical exponents of the momentum distribution near ${\mathit{k}}_{\mathit{F}}$ , 3 ${\mathit{k}}_{\mathit{F}}$ , and 5 ${\mathit{k}}_{\mathit{F}}$ are studied numerically for the one-dimensional U\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard model, using finite-size systems and extrapolating them to the thermodynamic limit. Results at ${\mathit{k}}_{\mathit{F}}$ agree with earlier calculations, while at 3 ${\mathit{k}}_{\mathit{F}}$ , exponents less than 1 are obtained for finite-size systems with extrapolation to 1 (regular behavior) in the thermodynamic limit, in contrast to the earlier analytic prediction of 9/8. The distribution is regular at 5 ${\mathit{k}}_{\mathit{F}}$ even for finite systems. The singularity near 3 ${\mathit{k}}_{\mathit{F}}$ is interpreted as due to low-energy excitations near 3 ${\mathit{k}}_{\mathit{F}}$ in finite systems. \textcopyright{} 1996 The American Physical Society.The critical exponents of the momentum distribution near ${\mathit{k}}_{\mathit{F}}$, 3${\mathit{k}}_{\mathit{F}}$, and 5${\mathit{k}}_{\mathit{F}}$ are studied numerically for the one-dimensional U\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard model, using finite-size systems and extrapolating them to the thermodynamic limit. Results at ${\mathit{k}}_{\mathit{F}}$ agree with earlier calculations, while at 3${\mathit{k}}_{\mathit{F}}$, exponents less than 1 are obtained for finite-size systems with extrapolation to 1 (regular behavior) in the thermodynamic limit, in contrast to the earlier analytic prediction of 9/8. The distribution is regular at 5${\mathit{k}}_{\mathit{F}}$ even for finite systems. The singularity near 3${\mathit{k}}_{\mathit{F}}$ is interpreted as due to low-energy excitations near 3${\mathit{k}}_{\mathit{F}}$ in finite systems. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterJul 15, 19967 citations

Tomonaga-Luttinger Liquid Exponents of Correlation Functions around Fermi points in the Hubbard Model

Nelson Oyindenyifa Nenuwe, J. O. A. Idiodi

The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical exponents for the model in the presence of a magnetic field are established by solving the dressed charge matrix equations and setting the number of occupancies to one, as an alternative to the usual zero often used by authors in literatures. Our result shows the critical exponents of the correlation function grows monotonically with magnetic field and reduces to definite values at zero magnetic field around various Fermi points.The correlation functions of one-dimensional Hubbard model in the presence of external magnetic field was investigated through the conformal field technique. The long distance behaviour of the correlation functions and their critical exponents for the model in the presence of a magnetic field are established by solving the dressed charge matrix equations and setting the number of occupancies to one, as an alternative to the usual zero often used by authors in literatures. Our result shows the critical exponents of the correlation function grows monotonically with magnetic field and reduces to definite values at zero magnetic field around various Fermi points.

arXiv:1507.07254Advances in physics theories and applicationsJul 26, 20150 citations

Critical exponents for the one-dimensional Hubbard model

Holger Frahm, V. E. Korepin

Using results on the scaling of energies with the size of the system and the principles of conformal quantum field theory, we calculate the asymptotics of correlation functions for the one-dimensional Hubbard model in the repulsive regime in the presence of an external magnetic field. The critical exponents are given in terms of a dressed charge matrix that is defined in terms of a set of integral equations obtained from the Bethe-Ansatz solution for the Hubbard model. An interpretation of this matrix in terms of thermodynamical coefficients is given, and several limiting cases are considered.Using results on the scaling of energies with the size of the system and the principles of conformal quantum field theory, we calculate the asymptotics of correlation functions for the one-dimensional Hubbard model in the repulsive regime in the presence of an external magnetic field. The critical exponents are given in terms of a dressed charge matrix that is defined in terms of a set of integral equations obtained from the Bethe-Ansatz solution for the Hubbard model. An interpretation of this matrix in terms of thermodynamical coefficients is given, and several limiting cases are considered.

Physical review. B, Condensed matterDec 1, 1990502 citations

Tomonaga-Luttinger Unusual Exponents around Fermi Points in the One-Dimensional Hubbard Model

Nelson Oyindenyifa Nenuwe, J. O. A. Idiodi

We study the correlation functions of one-dimensional Hubbard model in the presence of external magnetic field through the conformal field method. The long distance behaviour of the correlation functions and their unusual exponents for the model in the presence of a magnetic field are developed by solving the dressed charge matrix equations and setting the number of occupancies to one, as alternative to the usual zero used by authors in literatures. This work shows that the exponent of the correlation functions is a monotonous function of magnetic field and the correlation functions decay as powers of these unusual exponents. As the magnetic field goes to zero, we obtain the exponents as 8.125, 11.125, 17.125, 26.125 and 38.125 at kF, 3kF, 5kF, 7kF and 9kF. Our analytical results will provide insights into criticality in condensed matter physics.We study the correlation functions of one-dimensional Hubbard model in the presence of external magnetic field through the conformal field method. The long distance behaviour of the correlation functions and their unusual exponents for the model in the presence of a magnetic field are developed by solving the dressed charge matrix equations and setting the number of occupancies to one, as alternative to the usual zero used by authors in literatures. This work shows that the exponent of the correlation functions is a monotonous function of magnetic field and the correlation functions decay as powers of these unusual exponents. As the magnetic field goes to zero, we obtain the exponents as 8.125, 11.125, 17.125, 26.125 and 38.125 at kF, 3kF, 5kF, 7kF and 9kF. Our analytical results will provide insights into criticality in condensed matter physics.

World Journal of Condensed Matter PhysicsJan 1, 20151 citation

Magnetic-field effects on the correlation functions in the one-dimensional strongly correlated Hubbard model

Masao Ogata, Tadao Sugiyama, Hiroyuki Shiba

The momentum distribution function and spin-correlation functions are studied for the one-dimensional large-U Hubbard model with an emphasis on the effects of the magnetic field. A direct calculation of the correlation functions is carried out with the exact wave function, whose explicit form for the large-U limit was derived in a previous paper. Singularities are detected at ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$ and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$+2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$ in the momentum distribution function ${\mathit{n}}_{\mathrm{\ensuremath{\sigma}}}$(k), where ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$ is the Fermi wave number of the noninteracting electrons with a given magnetization. Similarly, the longitudinal spin-correlation function ${\mathit{S}}^{\mathit{z}\mathit{z}}$ (k) has singularities at 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$ and 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$, while the transverse one ${\mathit{S}}^{\mathit{x}\mathit{x}}$ (k) is singular at ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$ and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$-${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$. The nature of the singularities (i.e., critical exponents) is determined from an analysis of the size dependence. As a complementary approach, those critical exponents for the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit are explicitly calculated with conformal field theory. In this limit the exponents depend only on the magnetization and are independent of the electron density. The resulting exponents are consistent with the first results.The momentum distribution function and spin-correlation functions are studied for the one-dimensional large-U Hubbard model with an emphasis on the effects of the magnetic field. A direct calculation of the correlation functions is carried out with the exact wave function, whose explicit form for the large-U limit was derived in a previous paper. Singularities are detected at ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$ and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$+2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$ in the momentum distribution function ${\mathit{n}}_{\mathrm{\ensuremath{\sigma}}}$(k), where ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\sigma}}}$ is the Fermi wave number of the noninteracting electrons with a given magnetization. Similarly, the longitudinal spin-correlation function ${\mathit{S}}^{\mathit{z}\mathit{z}}$(k) has singularities at 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$ and 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$, while the transverse one ${\mathit{S}}^{\mathit{x}\mathit{x}}$(k) is singular at ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$ and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$-${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$. The nature of the singularities (i.e., critical exponents) is determined from an analysis of the size dependence. As a complementary approach, those critical exponents for the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit are explicitly calculated with conformal field theory. In this limit the exponents depend only on the magnetization and are independent of the electron density. The resulting exponents are consistent with the first results.

Physical review. B, Condensed matterApr 1, 199155 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

The critical exponents of the momentum distribution near

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

, 3

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

, and 5

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

are studied numerically for the one-dimensional U\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard model, using finite-size systems and extrapolating them to the thermodynamic limit. Results at

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

agree with earlier calculations, while at 3

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

, exponents less than 1 are obtained for finite-size systems with extrapolation to 1 (regular behavior) in the thermodynamic limit, in contrast to the earlier analytic prediction of 9/8. The distribution is regular at 5

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

even for finite systems. The singularity near 3

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

is interpreted as due to low-energy excitations near 3

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

in finite systems. \textcopyright{} 1996 The American Physical Society.

{\mathit{S}}^{\mathit{z}\mathit{z}}

(k) has singularities at 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$ and 2${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$, while the transverse one

{\mathit{S}}^{\mathit{x}\mathit{x}}

(k) is singular at ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$ and ${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\uparrow}}}$-${\mathit{k}}_{\mathit{F}\mathrm{\ensuremath{\downarrow}}}$. The nature of the singularities (i.e., critical exponents) is determined from an analysis of the size dependence. As a complementary approach, those critical exponents for the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit are explicitly calculated with conformal field theory. In this limit the exponents depend only on the magnetization and are independent of the electron density. The resulting exponents are consistent with the first results.

{\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.