Physical review. B, Condensed matter

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

Shaojin Qin, Lu Yu

Published Jul 15, 1996• 7 citations

Abstract

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.

DOI: 10.1103/physrevb.54.1447

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Physical review. B, Condensed matter

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

Shaojin Qin, Lu Yu

Published Jul 15, 1996• 7 citations

Publisher

Abstract

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.

DOI: 10.1103/physrevb.54.1447

Related papers

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

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JOURNAL OF ADVANCES IN PHYSICSNov 20, 20150 citations

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

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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

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}}

{\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{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.

{\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.