# On the scaling behaviour of the alternating spin chain

## TL;DR

This paper investigates the critical behavior of a 1D integrable spin chain with a continuous spectrum, linking Bethe state density calculations to differential equations and discussing finite size effects.

## Contribution

It introduces a novel approach to compute Bethe state densities via connection coefficients of differential equations with monodromy properties similar to confluent hypergeometric equations.

## Key findings

- Density of Bethe states related to differential equation monodromy
- Finite size corrections to scaling analyzed
- Critical behavior governed by a CFT with continuous spectrum

## Abstract

In this note we report the results of our study of a 1D integrable spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions. It is argued that the computation of the density of Bethe states of the continuous theory can be reduced to the calculation of the connection coefficients for a certain class of differential equations whose monodromy properties are similar to those of the conventional confluent hypergeometric equation. The finite size corrections to the scaling are also discussed.