Many-body Lattice Wavefunctions From Conformal Blocks

TL;DR

This paper presents a new framework for constructing many-body lattice wavefunctions using conformal blocks from rational conformal field theories, connecting lattice models with conformal field theory structures.

Contribution

It introduces a general method to derive lattice wavefunctions from RCFT conformal blocks, including novel applications to the Ising RCFT and its relation to the ITF spin chain.

Findings

Revisited the Haldane-Shastry model using this framework.

Established a connection between the Ising RCFT wavefunctions and the ITF spin chain.

Provided evidence that the ITF ground state matches the conformal block wavefunction.

Abstract

We introduce a general framework to construct many-body lattice wavefunctions starting from the conformal blocks (CBs) of rational conformal field theories (RCFTs). We discuss the different ways of encoding the physical degrees of freedom of the lattice system using both the internal symmetries of the theory and the fusion channels of the CBs. We illustrate this construction both by revisiting the known Haldane-Shastry model and by providing a novel implementation for the Ising RCFT. In the latter case, we find a connection to the Ising transverse field (ITF) spin chain via the Kramers-Wannier duality and the Temperley-Lieb-Jones algebra. We also find evidence that the ground state of the finite-size critical ITF Hamiltonian corresponds exactly to the wavefunction obtained from CBs of spin fields.