Excited States in Spin Chains from Conformal Blocks

TL;DR

This paper presents a method to construct excited states in one-dimensional spin chains derived from conformal field theory, revealing a deep connection between the spectrum of these systems and their underlying CFT.

Contribution

The authors develop a novel approach to generate excited states in spin chains using conformal blocks and descendant fields, linking CFT structures to spin system spectra.

Findings

Constructed excited states from descendant fields in the spin chain model.

Established the equivalence of the resulting system to the Haldane-Shastry model.

Highlighted the potential to extend this method to other model systems.

Abstract

We develop a method of constructing excited states in one dimensional spin chains which are derived from the $SU(2)_1$ Wess-Zumino-Witten Conformal Field Theory (CFT) using a parent Hamiltonian approach. The resulting systems are equivalent to the Haldane-Shastry model. In our ansatz, correlation functions between primary fields correspond to the ground state of the spin system, whereas excited states are obtained by insertion of descendant fields. Our construction is based on the current algebra of the CFT and emphasizes the close relation between the spectrum of the spin system and the underlying CFT. This general structure might imply that the method could be applied to a wider range of model systems.