Magnetic Field Effects on Correlation Functions in One-Dimensional Strongly Correlated Hubbard Model

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

Correlation functions of the one-dimensional Hubbard model

N. M. Bogoliubov, V. E. Korepin

Theoretical and Mathematical PhysicsMar 1, 199016 citations

Correlation functions of the one-dimensional Hubbard model in a magnetic field

Holger Frahm, V. E. Korepin

We present a general method for the calculation of correlation functions in the repulsive one-dimensional Hubbard model at less than half-filling in a magnetic field h. We describe the dependence of the critical exponents that drive their long-distance asymptotics on the Coulomb coupling, the density, and h. This dependence can be described in terms of a set of coupled Bethe-Ansatz integral equations. It simplifies significantly in the strong-coupling limit, where we give explicit formulas for the dependence of the critical exponents on the magnetic field. In particular, we find that at small field the functional dependence of the critical exponents on h can be algebraic or logarithmic---depending on the operators involved. In addition, we evaluate the singularities of the Fourier images of the correlation functions. It turns out that switching on a magnetic field gives rise to singularities in the dynamic field-field correlation functions that are absent at h=0.We present a general method for the calculation of correlation functions in the repulsive one-dimensional Hubbard model at less than half-filling in a magnetic field h. We describe the dependence of the critical exponents that drive their long-distance asymptotics on the Coulomb coupling, the density, and h. This dependence can be described in terms of a set of coupled Bethe-Ansatz integral equations. It simplifies significantly in the strong-coupling limit, where we give explicit formulas for the dependence of the critical exponents on the magnetic field. In particular, we find that at small field the functional dependence of the critical exponents on h can be algebraic or logarithmic---depending on the operators involved. In addition, we evaluate the singularities of the Fourier images of the correlation functions. It turns out that switching on a magnetic field gives rise to singularities in the dynamic field-field correlation functions that are absent at h=0.

Advanced series in mathematical physicsMay 1, 19940 citations

Correlation functions in the one-dimensional Hubbard model

A. M. Finkel'Shteǐn

Advanced series in mathematical physicsMay 1, 19942 citations

Correlation functions of the one-dimensional Hubbard model in a magnetic field

Holger Frahm, V. E. Korepin

Physical review. B, Condensed matterMar 1, 1991202 citations

Correlation Functions for the Two-Dimensional Hubbard Model

J. M. P. Carmelo, D. Baeriswyl, X. Zotos

NATO ASI series. Series B : PhysicsJan 1, 19890 citations

{\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.