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.

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Interacting anyons in topological quantum liquids: The golden chain
• Topological Defects on the Lattice I: The Ising model
• Simulation of anyons with tensor network algorithms
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Infinite Matrix Product States for long range SU(N) spin models
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Chiral correlators of the Ising conformal field theory
• Excited States in Spin Chains from Conformal Blocks
• Construction of spin models displaying quantum criticality from quantum field theory

Cited by in corpus (4)

• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Kramers-Wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• The BCS wave function, matrix product states, and the Ising conformal field theory