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Physical review. B, Condensed matter

Exactly solvable model with spin-triplet pairs and magnetic correlations

Andrei A. Zvyagin, P. Schlottmann

Published Sep 1, 1999• 6 citations
Publisher

Abstract

We consider an exactly solvable two-band model of electrons moving in one dimension and interacting with a $\ensuremath{\delta}$-function spin-exchange potential. The relative population of the bands is determined by the band splitting, the magnetic field, and the temperature. The interaction leads to the formation of spin-triplet bound states of the Cooper type (hard-core bosons that do not condensate and exist at all temperatures). In the zero-field ground state the spin-triplet states are effectively free bosons. A threshold band splitting is required to break up a triplet pair. The low-temperature and finite size properties are discussed in the context of anomalous superconducting and antiferromagnetic fluctuations.

DOI
10.1103/physrevb.60.6292

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We consider an exactly solvable two-band model of electrons moving in one dimension and interacting with a \ensuremathδ\ensuremath{\delta}\ensuremathδ-function spin-exchange potential. The relative population of the bands is determined by the band splitting, the magnetic field, and the temperature. The interaction leads to the formation of spin-triplet bound states of the Cooper type (hard-core bosons that do not condensate and exist at all temperatures). In the zero-field ground state the spin-triplet states are effectively free bosons. A threshold band splitting is required to break up a triplet pair. The low-temperature and finite size properties are discussed in the context of anomalous superconducting and antiferromagnetic fluctuations.
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.
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.
A model of hard-core bosons and spin-1 sites with single-ion anisotropy is proposed to approximately describe hole pairs moving in a background of singlets and triplets with the aim of exploring the relationship between superconductivity and antiferromagnetism. The properties of this model at zero temperature were investigated using quantum Monte Carlo techniques. The most important feature found is the suppression of superconductivity, as long range coherence of preformed pairs, due to the presence of both antiferromagnetism and ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1$ excitations. Indications of charge ordered and other phases are also discussed.
The thermodynamic Bethe-ansatz equations for the one-dimensional Hubbard model with attractive on-site interaction of the electrons are solved numerically at low temperatures. At low temperatures the dominant states consist of spin-paired electrons (Cooper-pair--like) and excitations of such pairs (without breaking up the singlet bound states). A critical field (energy required to depair a Cooper pair) is obtained at T=0 (note that the superconducting Tc{T}_{c}Tc​=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.
We consider the coexistence of the Hund's-rule-exchange induced spin-triplet paired state with the antiferromagnetic ordering by starting from the extended Hubbard model for a doubly degenerate band.We use the density of states appropriate for the square lattice and treat the problem in the HartreeFock approximation.The temperature dependences of the superconducting gaps, the magnetic moment, and the chemical potential are presented.The free energy in the considered phase is evaluated, as well as the corresponding free energies in four additional phases: paramagnetic, ferromagnetic, superconducting of type A and superconducting of type A1 coexisting with ferromagnetism; they occur in the proper range of parameters: band lling n and the interaction parameters U/W and J/W .The low temperature values of the superconducting gaps and staggered magnetic moment are also analyzed as a function of band lling.
The two-band model describing strongly hybridized degenerated electron states in a chain is proposed and solved exactly by means of the Bethe ansatz. The fermions of the subbands interact with each other via one-particle and one-particle correlated on-site hybridized interactions. The chain of electrons is reduced to the model with two noninteracting subbands with a given total number of electrons, in which fermions interact via different effective constants of interactions. In the case of strong hybridized interaction the on-site repulsive interaction is compensated by hybridized interaction, which leads to an effective attractive interaction between particles and the formation of spinless bound states of Cooper type. This electron liquid component determines both heavy fermion- and superconducting-type behavior of electron properties.