A distribution approach to finite-size corrections in Bethe Ansatz solvable models

TL;DR

The paper introduces a new distribution-based method to efficiently compute finite-size effects in Bethe Ansatz solvable models, exemplified on the XXZ spin chain, recovering key conformal data.

Contribution

It develops a novel functional approach to derive finite-size corrections applicable to models solvable by Bethe Ansatz, generalizing previous techniques.

Findings

Derived finite-size corrections for the XXZ chain's leading eigenvalues

Recovered expected conformal charge and dimensions

Presented a generalizable method for Bethe Ansatz models

Abstract

We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe roots. A simple and powerful constraint is derived when applying this functional to infinitely derivable test functions with compact support, that generalizes then to more general test functions. The method is presented in the context of the simple spin-$1/2$ XXZ chain for which we derive the finite-size corrections to leading eigenvalues of the Hamiltonian for any configuration of Bethe numbers with real Bethe roots. The expected results for the central charge and conformal dimensions are recovered.