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arXiv · 1609.05217

Many-body Lattice Wavefunctions From Conformal Blocks

Sebastian Montes·Javier Rodríguez-Laguna·Hong-Hao Tu·Germán Sierra
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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.

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Sebastian Montes, Javier Rodríguez-Laguna, Hong-Hao Tu, Germán Sierra. 2016-12-29. Many-body Lattice Wavefunctions From Conformal Blocks. https://doi.org/10.1103/physrevb.95.085146

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