Characters for $\hat{sl(n)}_{k=1}$ from a novel Thermodynamic Bethe Ansatz

TL;DR

This paper introduces a new thermodynamic Bethe ansatz approach to derive characters of affine Lie algebra sl(n) at level 1, linking fractional statistics and spinon character formulas, with proofs based on Durfee rectangle combinatorics.

Contribution

It presents a novel quasi-particle formula for sl(n) level 1 characters derived from thermodynamic Bethe ansatz, connecting fractional statistics and providing combinatorial proofs.

Findings

Derived quasi-particle formulas for sl(n) characters

Established connection to fractional statistics in 1D quantum systems

Provided combinatorial proof using Durfee rectangle formula

Abstract

Motivated by the recent development on the exact thermodynamics of 1D quantum systems, we propose quasi-particle like formulas for $\hat{\mathfrak{sl}(n)}_{k=1}$ characters. The $\hat{\mathfrak{sl}(2)}_{k=1}$ case is re-examined first. The novel formulation yields a direct connection to the fractional statistics in the short range interacting model, and provides a clear description of the spinon character formula. Generalizing the observation, we find formulas for $\hat{\mathfrak{sl}(n)}_{k=1}$, which can be proved by the Durfee rectangle formula.