Excitations and S-matrix for su(3) spin chain combining ${3}$ and ${3^{*}}

TL;DR

This paper analyzes the su(3) spin chain combining 3 and 3* representations, deriving the Hamiltonian, solving the ansatz equations, and calculating the exact S matrix for two-hole states, providing insights into excitations and ground state properties.

Contribution

It introduces the Hamiltonian and solves the ansatz equations for the su(3) chain with 3 and 3* representations, and computes the exact S matrix for two-hole excitations.

Findings

Derived the Hamiltonian for the su(3) chain with 3 and 3* representations.

Solved the ansatz equations in the thermodynamic limit.

Calculated the exact S matrix for two-hole states.

Abstract

The associated Hamiltonian for a su(3) spin chain combining ${3}$ and ${3^{*}}$ representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found . The excited states are characterized by means of these quantum numbers. Finally, the exact S matrix for a state with two holes is found.