Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models

TL;DR

This paper constructs lattice analogues of Moore-Read states for bosons and fermions, demonstrates their topological properties, and derives exact parent Hamiltonians, bridging continuum and lattice models of non-Abelian quantum Hall states.

Contribution

It introduces a family of lattice Moore-Read states, analyzes their topological features, and provides exact parent Hamiltonians and local models for these states.

Findings

Topological entanglement entropy remains constant along the interpolation.

Lattice Moore-Read states exhibit the same topological properties as continuum states.

Exact parent Hamiltonians are derived for these lattice states.

Abstract

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.