Abstract
In this work, we have studied the invariants of motion of two SU(N) supersymmetric t-J models of 1/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 to 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.
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As in Ref. [5], Eq. (4) identifies the t-J model with the intrinsic dynamic pairs, in the strong interaction limit, of the integrable continuous system H = 1/2∑ L i=1 P 2 i + ∑i> j[1(1-M ij )]/[d 2(x i - X j )] for a mixture of Q spinless bosons and N e fermions with spins.
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Wang, D.F., Gruber, C. (1994). Invariants of the 1/r 2 Supersymmetric t-J Models. In: Khuri, R.R., Liu, J.T., Chen, F., Gan, W. (eds) The Universality of Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0585-3_14
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DOI: https://doi.org/10.1007/978-1-4615-0585-3_14
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