Physical Review Letters

Anomalous low-temperature properties of the degenerate one-dimensional Hubbard model

Kong-Ju-Bock Lee, P. Schlottmann

Published Nov 13, 1989• 26 citations

Abstract

Unusual properties of the Hubbard chain of arbitrary degeneracy N and excluded-site occupations of more than two electrons are presented: (i) In zero field and in the limit of large N the ground state resembles an interacting Bose gas. The 1/N contributions vanish identically, so that corrections to leading order are 1/${\mathrm{N}}^{2}$. (ii) The susceptibility at T=0 shows logarithmic singularities as H\ensuremath{\rightarrow}0. (iii) The Hubbard model and the Heisenberg chain have the same low-energy spin excitations for all U. (iv) The specific-heat coefficient \ensuremath{\gamma} is singular. These properties hold for arbitrary band filling and (ii)--(iv) hold for all N\ensuremath{\ge}2.

DOI: 10.1103/physrevlett.63.2299

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Physical Review Letters

Anomalous low-temperature properties of the degenerate one-dimensional Hubbard model

Kong-Ju-Bock Lee, P. Schlottmann

Published Nov 13, 1989• 26 citations

Publisher

Abstract

{\mathrm{N}}^{2}

. (ii) The susceptibility at T=0 shows logarithmic singularities as H\ensuremath{\rightarrow}0. (iii) The Hubbard model and the Heisenberg chain have the same low-energy spin excitations for all U. (iv) The specific-heat coefficient \ensuremath{\gamma} is singular. These properties hold for arbitrary band filling and (ii)--(iv) hold for all N\ensuremath{\ge}2.

DOI: 10.1103/physrevlett.63.2299

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Spin and charge excitations of the degenerate Hubbard model in one dimension

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The degenerate Hubbard chain with N internal degrees of freedom is integrable if site occupations of more than two electrons are excluded. The ground state of the model has several unusual properties; e.g., the magnetic susceptibility has logarithmic singularities as the field H\ensuremath{\rightarrow}0 and also the specific-heat coefficient is singular. An extensive discussion of ground-state properties as a function of U and the band filling is presented. The elemental charge and spin excitations are derived for arbitrary U and band filling. If, on average, there is exactly one electron per site as a function of U, a qualitative change in the low-energy charge excitations is found at a critical value ${\mathit{U}}_{\mathit{c}}$ . This change is probably associated with a Mott metal-insulator transition ( ${\mathit{U}}_{\mathit{c}}$ =0 for N=2). The Fermi velocity is finite for U ${\mathit{U}}_{\mathit{c}}$ but vanishes for U> ${\mathit{U}}_{\mathit{c}}$ (for one electron per site). The spin-wave velocity is inversely proportional to the magnetic susceptibility for all U and band fillings. There are N-1 elemental spin-wave branches. For arbitrary band filling there are then N-1 soft modes at different finite momenta, all related to the Fermi surface. For exactly one electron per site, the spin-excitation spectrum can be mapped onto the one of the SU(N) Heisenberg chain. The implications of the hole states on superconductivity are also discussed.The degenerate Hubbard chain with N internal degrees of freedom is integrable if site occupations of more than two electrons are excluded. The ground state of the model has several unusual properties; e.g., the magnetic susceptibility has logarithmic singularities as the field H\ensuremath{\rightarrow}0 and also the specific-heat coefficient is singular. An extensive discussion of ground-state properties as a function of U and the band filling is presented. The elemental charge and spin excitations are derived for arbitrary U and band filling. If, on average, there is exactly one electron per site as a function of U, a qualitative change in the low-energy charge excitations is found at a critical value ${\mathit{U}}_{\mathit{c}}$. This change is probably associated with a Mott metal-insulator transition (${\mathit{U}}_{\mathit{c}}$=0 for N=2). The Fermi velocity is finite for U${\mathit{U}}_{\mathit{c}}$ but vanishes for U>${\mathit{U}}_{\mathit{c}}$ (for one electron per site). The spin-wave velocity is inversely proportional to the magnetic susceptibility for all U and band fillings. There are N-1 elemental spin-wave branches. For arbitrary band filling there are then N-1 soft modes at different finite momenta, all related to the Fermi surface. For exactly one electron per site, the spin-excitation spectrum can be mapped onto the one of the SU(N) Heisenberg chain. The implications of the hole states on superconductivity are also discussed.

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Physical review. B, Solid stateMar 1, 1972201 citations

{\mathrm{N}}^{2}

{\mathit{U}}_{\mathit{c}}

. This change is probably associated with a Mott metal-insulator transition (

{\mathit{U}}_{\mathit{c}}

=0 for N=2). The Fermi velocity is finite for U

{\mathit{U}}_{\mathit{c}}

but vanishes for U>

{\mathit{U}}_{\mathit{c}}

(for one electron per site). The spin-wave velocity is inversely proportional to the magnetic susceptibility for all U and band fillings. There are N-1 elemental spin-wave branches. For arbitrary band filling there are then N-1 soft modes at different finite momenta, all related to the Fermi surface. For exactly one electron per site, the spin-excitation spectrum can be mapped onto the one of the SU(N) Heisenberg chain. The implications of the hole states on superconductivity are also discussed.

{T}_{c}

=0), which disappears for T\ensuremath{\ne}0. The specific heat is linear in temperature, and the dependence of the coefficient \ensuremath{\gamma} on band filling and magnetic field is discussed. The excitation spectrum shows some analogies with that of resonant valence bonds in two dimensions.

{\mathit{U}}_{\mathit{c}}

of the Coulomb repulsion.

{\mathit{U}}_{\mathit{c}}

depends on N (

{\mathit{U}}_{\mathit{c}}

=0 for N=2). A qualitative change in the charge-rapidity distribution is found at

{\mathit{U}}_{\mathit{c}}

. The Fermi velocity is finite for U

{\mathit{U}}_{\mathit{c}}

, diverges as U\ensuremath{\rightarrow}

{\mathit{U}}_{\mathit{c}}

, and vanishes for U>

{\mathit{U}}_{\mathit{c}}

U

to the total width $\ensuremath{\Delta}$ of the band of single-particle excitations is larger than 1, the specific heat has two peaks. The high-temperature peak arises from the gradual metal-insulator transition (or the gradual formation of local moments), while the low-temperature peak is associated with the antiferromagnetic short-range ordering. When $\frac{U}{\ensuremath{\Delta}}$ becomes small, the two peaks merge into one. This picture is consistent with all other thermal properties, including correlation functions. The high-temperature properties are compared with the results predicted by Hubbard's approximate theory based on the truncation of the equations of motion of the Green's functions.