Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Modern Physics Letters B

INTEGRABLE TWO-PARAMETER MODEL OF THE FERMI GAS

Igor N. Karnaukhov

Published Mar 20, 1996• 0 citations
Publisher

Abstract

We present a two-band model of the gas of fermions consisting of a parabolic band of conduction electrons and a band of local pairs interacting via a δ-function interband interaction. The model is integrable and its solution has been obtained by means of the Bethe ansatz. The ground state energy and the density of conduction electrons have been calculated numerically.

DOI
10.1142/s0217984996000328

Related papers

New Exactly Solvable One-Parameter Model of Strongly Correlated Electrons

Igor N. Karnaukhov

We present a two band fermion model consisting of a subband of conduction electrons and a subband of local electron pairs interacting via interband interactions. The model is solved in one dimension by means of the Bethe ansatz for an empty subband of local electron pairs. The ground state energy, the chemical potential, the critical exponents, describing the asymptotic behavior of correlation functions at long distances, the effective electron transport mass have been calculated numerically for an arbitrary density of conduction electrons.

International Journal of Modern Physics B•Dec 10, 1997•0 citations

Exact solution of a two-chain model of fermions

Igor N. Karnaukhov

We present a two sublattice model of fermions consisting of a chain of conduction electrons and a chain of local pairs interacting via an interlattice interaction. The model is integrable for some special values of the coupling constants and its solution has been obtained by means of the Bethe ansatz. The effective transport mass has been calculated numerically for an arbitrary density of conduction electrons. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Jul 1, 1996•2 citations

A soluble model for the formation of exciton bands and electron-hole droplets in one dimension

P. Schlottmann

We consider an integrable model consisting of two one-dimensional parabolic bands of opposite mass (m=+or- 1/2 , respectively) separated by a gap, 2 Delta . The bands contain spinless fermions, one band corresponds to the conduction band and the other one to the valence band of a semiconductor or semimetal. The holes in the valence band and the spinless electrons in the conduction band are locally attracted via a delta -function potential. This model can be mapped onto the two-component Fermi gas with delta -function interaction, so that the two components label the bands: the chemical potential corresponds to a magnetic field, and Delta to the chemical potential. We use Gaudin and Yang's exact solution of the many-body problem to study the formation of exciton bands. The properties of the ground and metastable states, the excitation spectrum and the thermodynamics of the model are obtained. In the ground or metastable states the particles (electrons in the conduction band and holes in the valence band) are either paired in exciton bound states or unpaired. Their spectrum of elemental excitations is approximately parabolic. At finite T many-particle bound states (string solutions of the Bethe ansatz equations) can be populated; at low T these states are strongly delocalized and can be interpreted as electron-hole droplets. The low-T properties of the model are discussed.

Journal of Physics Condensed Matter•May 16, 1994•4 citations

Integrable two-band model with attractive and repulsive interactions

P. Schlottmann

The exact solution via Bethe's ansatz to a model consisting of two parabolic bands of electrons with local attractive and repulsive interactions is presented. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic field, and the crystal-field splitting between the bands. The attractive interaction leads to Cooper-pair-like bound states and a threshold magnetic field is required to overcome the binding energy. The low-T specific heat is proportional to T, except at critical points where C\ensuremath{\propto}${\mathit{T}}^{1/2}$.

Physical Review Letters•Mar 23, 1992•37 citations

Thermodynamics of the one-dimensional multicomponent Fermi gas with a delta -function interaction

P. Schlottmann

The author considers a gas of fermions with parabolic dispersion and N spin-components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. He analyses the discrete Bethe ansatz equations and classifies their solutions according to the string hypothesis. The thermodynamic Bethe-ansatz equations are derived for arbitrary band-filling for both repulsive and attractive interaction in terms of the thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are then discussed in several limiting cases, e.g. S=1/2, the ground state (T to 0), for vanishing interaction strength, for strong coupling, in the high-temperature limit, and the large-N limit.

Journal of Physics Condensed Matter•Aug 9, 1993•33 citations

Two-band model with attractive and repulsive interactions in one dimension: Ground state, excitations, and thermodynamics

P. Schlottmann

We present the exact solution via Bethe's ansatz to an integrable model consisting of two parabolic bands of electrons of equal mass with a local \ensuremath{\delta}-function exchange interaction. The interaction is attractive or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet state. The structure of the Bethe ansatz and the classification of states is similar to the one of the two-channel Kondo problem. The interest in two-band models arises from the possibility that both the 3${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ and 3${\mathit{d}}_{\mathit{z}}^{2}$ orbitals may play a role in high-${\mathit{T}}_{\mathit{c}}$ cuprates. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic field, and the (crystalline field) splitting between the bands. The attractive interaction leads to Cooper-pair-like bound states, which exist at every temperature. There is no long-range order and no condensation of the Cooper pairs. A threshold magnetic field is required to overcome the binding energy of the Cooper pairs and there is no response to fields smaller than the critical one. The low-temperature specific heat is proportional to T, except at critical points (van Hove singularities of the bands) where C\ensuremath{\propto}${\mathit{T}}^{1/2}$. The spectrum of elemental excitations is approximately parabolic.

Physical review. B, Condensed matter•Mar 1, 1994•10 citations
We present a two-band model of the gas of fermions consisting of a parabolic band of conduction electrons and a band of local pairs interacting via a δ-function interband interaction. The model is integrable and its solution has been obtained by means of the Bethe ansatz. The ground state energy and the density of conduction electrons have been calculated numerically.
We present a two band fermion model consisting of a subband of conduction electrons and a subband of local electron pairs interacting via interband interactions. The model is solved in one dimension by means of the Bethe ansatz for an empty subband of local electron pairs. The ground state energy, the chemical potential, the critical exponents, describing the asymptotic behavior of correlation functions at long distances, the effective electron transport mass have been calculated numerically for an arbitrary density of conduction electrons.
We consider an integrable model consisting of two one-dimensional parabolic bands of opposite mass (m=+or- 1/2 , respectively) separated by a gap, 2 Delta . The bands contain spinless fermions, one band corresponds to the conduction band and the other one to the valence band of a semiconductor or semimetal. The holes in the valence band and the spinless electrons in the conduction band are locally attracted via a delta -function potential. This model can be mapped onto the two-component Fermi gas with delta -function interaction, so that the two components label the bands: the chemical potential corresponds to a magnetic field, and Delta to the chemical potential. We use Gaudin and Yang's exact solution of the many-body problem to study the formation of exciton bands. The properties of the ground and metastable states, the excitation spectrum and the thermodynamics of the model are obtained. In the ground or metastable states the particles (electrons in the conduction band and holes in the valence band) are either paired in exciton bound states or unpaired. Their spectrum of elemental excitations is approximately parabolic. At finite T many-particle bound states (string solutions of the Bethe ansatz equations) can be populated; at low T these states are strongly delocalized and can be interpreted as electron-hole droplets. The low-T properties of the model are discussed.
The exact solution via Bethe's ansatz to a model consisting of two parabolic bands of electrons with local attractive and repulsive interactions is presented. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic field, and the crystal-field splitting between the bands. The attractive interaction leads to Cooper-pair-like bound states and a threshold magnetic field is required to overcome the binding energy. The low-T specific heat is proportional to T, except at critical points where C\ensuremath{\propto}T1/2{\mathit{T}}^{1/2}T1/2.
The author considers a gas of fermions with parabolic dispersion and N spin-components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. He analyses the discrete Bethe ansatz equations and classifies their solutions according to the string hypothesis. The thermodynamic Bethe-ansatz equations are derived for arbitrary band-filling for both repulsive and attractive interaction in terms of the thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are then discussed in several limiting cases, e.g. S=1/2, the ground state (T to 0), for vanishing interaction strength, for strong coupling, in the high-temperature limit, and the large-N limit.
We present the exact solution via Bethe's ansatz to an integrable model consisting of two parabolic bands of electrons of equal mass with a local \ensuremath{\delta}-function exchange interaction. The interaction is attractive or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet state. The structure of the Bethe ansatz and the classification of states is similar to the one of the two-channel Kondo problem. The interest in two-band models arises from the possibility that both the 3dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 and 3dz2{\mathit{d}}_{\mathit{z}}^{2}dz2​ orbitals may play a role in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates. Some low-temperature properties of this model are discussed as a function of the interaction strength, a magnetic field, and the (crystalline field) splitting between the bands. The attractive interaction leads to Cooper-pair-like bound states, which exist at every temperature. There is no long-range order and no condensation of the Cooper pairs. A threshold magnetic field is required to overcome the binding energy of the Cooper pairs and there is no response to fields smaller than the critical one. The low-temperature specific heat is proportional to T, except at critical points (van Hove singularities of the bands) where C\ensuremath{\propto}T1/2{\mathit{T}}^{1/2}T1/2. The spectrum of elemental excitations is approximately parabolic.