# A convenient basis for the Izergin-Korepin model

## TL;DR

This paper introduces a new orthogonal basis for the Izergin-Korepin model's Hilbert space, simplifying the monodromy-matrix elements and enabling recursive expressions for Bethe states, thus facilitating analysis of this quantum integrable system.

## Contribution

It develops a convenient orthogonal basis for the Izergin-Korepin model, simplifying operator actions and deriving recursive Bethe state expressions.

## Key findings

- Simplified monodromy-matrix element expressions in the new basis
- Recursive formulas for Bethe states derived
- Basis resembles the F-basis for A-type quantum chains

## Abstract

We propose a convenient orthogonal basis of the Hilbert space for the Izergin-Korepin model (or the quantum spin chain associated with the $A^{(2)}_{2}$ algebra). It is shown that the monodromy-matrix elements acting on the basis take relatively simple forms (c.f. acting on the original basis ), which is quite similar as that in the so-called F-basis for the quantum spin chains associated with $A$-type (super)algebras. As an application, we present the recursive expressions of Bethe states in the basis for the Izergin-Korepin model.