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

Abstract

Motivated by the recent development on the exact thermodynamics of 1D quantum systems, we propose quasi-particle like formulas for ${\widehat{\mathfrak{sl}(n)}}_{k=1}$ characters. The ${\widehat{\mathfrak{sl}(2)}}_{k=1}$ 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 ${\widehat{\mathfrak{sl}(n)}}_{k=1}$, which can be proved by the Durfee rectangle formula.

13 pages, Latex 2e

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Cited by in corpus (7)

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• Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model
• Exact Dynamics of the SU(K) Haldane-Shastry Model
• Exclusion statistics in conformal field theory and the UCPF for WZW models