Lattice Laughlin states on the torus from conformal field theory

Abstract

Conformal field theory has turned out to be a powerful tool to derive two-dimensional lattice models displaying fractional quantum Hall physics. So far most of the work has been for lattices with open boundary conditions in at least one of the two directions, but it is desirable to also be able to handle the case of periodic boundary conditions. Here, we take steps in this direction by deriving analytical expressions for a family of conformal field theory states on the torus that is closely related to the family of bosonic and fermionic Laughlin states. We compute how the states transform when a particle is moved around the torus and when the states are translated or rotated, and we provide numerical evidence in particular cases that the states become orthonormal up to a common factor for large lattices. We use these results to find the S-matrix of the states, which turns out to be the same as for the continuum Laughlin states. Finally, we show that when the states are defined on a square lattice with suitable lattice spacing they practically coincide with the Laughlin states restricted to a lattice.

20 pages, 1 figure, v2: accepted version

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Cited by in corpus (8)

• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
• Model wavefunctions for interfaces between lattice Laughlin states
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• Anyonic quasiparticles of hardcore anyons
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids