Invariants of the $1/r^2$ Supersymmetric t-J Models

Abstract

In this work, we have studied the invariants of motion of two SU(N) supersymmetric t-J model 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 non-equal 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. (IPT-EPFL 31/10/1993).

10 pages, Latex, IPT-EPFL 31/10/1993

References in corpus (9)

• Exchange Operator Formalism for Integrable Systems of Particles
• Lattice Integrable Systems of Haldane-Shastry Type
• On Models with Inverse-Square Exchange
• Solution of Some Integrable One-Dimensional Quantum Systems
• Spectrum of a spin chain with inverse square exchange
• Super Lax Pairs and Infinite Symmetries in The $1/r^2$ System
• Invariants of the Haldane-Shastry $SU(N)$ Chain
• Spectrum and Thermodynamics of the one-dimensional supersymmetric t-J model with $1/r^2$ exchange and hopping
• Solutions to the Multi-Component 1/R Hubbard Model

Cited by in corpus (5)

• Exact Results of the 1D $1/r^2$ Supersymmetric t-J Model without Translational Invariance
• Exactly solvable extended Hubbard model
• Quantum duality and Bethe-ansatz for the Hofstadter problem on hexagonal lattice
• Integrabilities of the long range t-J model of twisted boundary condition
• Spinless Calogero-Sutherland model with twisted boundary condition