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Physical Review Letters

Ground state and excitations of a one-dimensional two-band supersymmetrict-Jmodel with crystalline field splitting

P. Schlottmann

Published Oct 19, 1992• 12 citations
Publisher

Abstract

We consider a one-dimensional two-band model of electrons on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites, an interband splitting, \ensuremath{\Delta}, and intraband and interband exchange J between neighboring sites. This model is integrable at the supersymmetric point and reduces to the SU(4)-invariant supersymmetric t-J model with crystal field splitting. We present the exact solution via Bethe's ansatz and discuss ground-state properties and the excitation spectrum as a function of \ensuremath{\Delta}.

DOI
10.1103/physrevlett.69.2396

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Journal of Physics Condensed Matter•Sep 14, 1992•21 citations
We consider a one-dimensional two-band model of electrons on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites, an interband splitting, \ensuremath{\Delta}, and intraband and interband exchange J between neighboring sites. This model is integrable at the supersymmetric point and reduces to the SU(4)-invariant supersymmetric t-J model with crystal field splitting. We present the exact solution via Bethe's ansatz and discuss ground-state properties and the excitation spectrum as a function of \ensuremath{\Delta}.
The one-dimensional t−J model is considered, consisting of electrons with four spin-components on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the sites, exchange J between neighboring sites and a crystal field splitting Δ. This model is integrable at the supersymmetric point. The exact solution is presented via Bethe’s ansatz and groundstate properties as a function of Δ are discussed. The model could correspond to a two-band situation with one band being the z2 and the other one the x2−y2 orbitals of Cu2+.
The authors considers the one-dimensional SU(N)-invariant t-J model which consists of electrons with N spin components on a lattice with nearest-neighbour hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighbouring lattice sites. The model is integrable at the supersymmetric point t=J. The ground state Bethe ansatz equations are analysed and solved numerically for arbitrary band filling and several values of N. The ground state energy, the chemical potential and the spin susceptibility are obtained as a function of band filling. The elemental charge and spin excitations are derived for arbitrary N and band filling. The energy of the charge excitations vanishes at the Fermi surface. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. The spinwave velocity is inversely proportional to the susceptibility. For exactly one electron per site the charge fluctuations are suppressed and the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.
We consider the one-dimensional SU(N)-invariant t-J model, which consists of electrons with N spin components on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites and spin-exchange J between neighboring lattice sites. The model is integrable and has been diagonalized in terms of nested Bethe ansatze at the supersymmetric point t=J. The low-T specific heat is proportional to T. The γ-coefficient is extracted from the thermodynamic Bethe-ansatz equations and is expressed in terms of the spin wave velocities and the group velocity of the charges for arbitrary N, band filling, and splitting of the levels (magnetic and crystalline fields). Our results contain the following special cases: (i) For N=2 the traditional spin-1/2 supersymmetric t-J model, (ii) for exactly one electron per site the SU(N)-Heisenberg chain, and (iii) for N=4 the two-band supersymmetric t-J model with crystalline field splitting.
We consider a one-dimensional two-band model of electrons on a lattice with equal nearest-neighbour hopping, an interband splitting Delta and a Hubbard-like repulsion U. The model is defined via the SU(4) generalization of Lieb and Wu's Bethe ansatz solution of the one-dimensional Hubbard model. At T=0 the model has a Mott metal-insulator transition at a critical value U c ( Delta ) for a band filling of exactly one electron per site. U c decreases with Delta , being zero if the excited-electron band is empty, and U c =2.981 when the bands are degenerate. We discuss the ground-state properties, the spectrum of elemental excitations, the specific heat and the magnetic susceptibility, in both the metallic and insulating phases, as a function of the crystal-field splitting for exactly one electron per site. There are four branches of elemental excitations: (i) charge excitations, (ii) crystalline-field excitations and (iii) two branches of spin waves. The Fermi velocity is finite in the metallic phase, diverges as the metal-insulator transition is approached from the metallic side and vanishes for the insulator. Each band contributes to the susceptibility with a term that is inversely proportional to the spin-wave velocity for that band. The low-temperature specific heat is proportional to T and to the sum of the inverses of the velocities of the four branches.
We consider the one-dimensional t-J model, which consists of spin-1/2 electrons on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J=2t. We extend the model by introducing an impurity of arbitrary spin S that interacts with the electrons on the neighboring sites without destroying the integrability. The lattice model is defined by the scattering matrices via the quantum inverse scattering method. The interaction Hamiltonian between the impurity and the itinerant electrons is only explicitly constructed in the continuum limit. The discrete Bethe ansatz equations diagonalizing the model are derived and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived and the impurity free energy is obtained for arbitrary bandfilling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter. The impurity can localize up to one itinerant electron and has in general mixed valent properties. The integer valent low T small H fixed point of the impurity corresponds to an asymptotically free spin S, while if either T or H (or both) become large the impurity behaves like an asymptotically free spin (S+).
The one-dimensional SU(N)-invariant t-J model consists of electrons with N spin components on a lattice with nearest-neighbour hopping and spin exchange J. The multiple occupancy of the lattice sites is excluded. The model is integrable at the supersymmetric point, t=J. The discrete Bethe ansatz equations are analysed and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived for arbitrary band filling in terms of thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are solved in limiting cases, e.g., S=1/2, the ground state and the high-temperature limit. If the charge fluctuations are suppressed the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.