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arXiv:cond-mat/9311041 · Physical review. B, Condensed matter

Invariants of the 1/ r2 supersymmetrict-Jmodels

D. F. Wang, C. Gruber

Published Jun 1, 1994• 13 citations
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Abstract

In this work, we have studied the invariants of motion of two SU(N) supersymmetric t-J models of 1/${\mathit{r}}^{2}$ hopping and exchange in one dimension. The first model is defined on a lattice of equal spaced sites, and the second on a nonequal spacing lattice. Using the ``exchange operator formalism,'' we are able to construct all the invariants for the models, by mapping the systems onto mixtures of fermions and bosons. This identification shows that the supersymmetric t-J model on the chain with equal-spaced sites also belongs to Shastry-Sutherland's ``super-lax-pair'' family.

DOI
10.1103/physrevb.49.15712

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Physical Review Letters•Oct 19, 1992•12 citations
In this work, we have studied the invariants of motion of two SU(N) supersymmetric t-J models of 1/r2{\mathit{r}}^{2}r2 hopping and exchange in one dimension. The first model is defined on a lattice of equal spaced sites, and the second on a nonequal spacing lattice. Using the exchange operator formalism,'' we are able to construct all the invariants for the models, by mapping the systems onto mixtures of fermions and bosons. This identification shows that the supersymmetric t-J model on the chain with equal-spaced sites also belongs to Shastry-Sutherland's super-lax-pair'' family.
In this work, we continue the study of the supersymmetric t-J model with 1/r2{\mathit{r}}^{2}r2 hopping and exchange without translational invariance. A set of Jastrow eigenfunctions are obtained for the system, with eigenenergies explicitly calculated. The ground state of the t-J model is included in this set of wave functions. The spectrum of this t-J model consists of equidistant energy levels which are highly degenerate.
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.
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in one dimension and belong to the 1/r2{\mathit{r}}^{2}r2 family of interactions. The algebra consists of the commutation between a ``super-Hamiltonian'' and two other operators, in an enlarged Hilbert space. These reduce to quantal Ordered Lax equations when projected onto the original subspace, and to a statement about the ``Harmonic Lattice Potential'' structure of the Lax operator, leading to a highly automatic proof of the integrability of these models and to an interesting hierarchy of new models.
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 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}.