Many-body Lattice Wavefunctions From Conformal Blocks
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.
Keywords
Cite
@article{arxiv.1609.05217,
title = {Many-body Lattice Wavefunctions From Conformal Blocks},
author = {Sebastian Montes and Javier Rodríguez-Laguna and Hong-Hao Tu and Germán Sierra},
journal= {arXiv preprint arXiv:1609.05217},
year = {2017}
}