Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization

TL;DR

This paper develops and optimizes short-range Hamiltonians for spin-1 kagome systems that closely approximate non-Abelian topological states, using truncation and numerical methods to achieve high overlaps with theoretical Moore-Read states.

Contribution

It introduces a truncation and optimization procedure to derive short-range Hamiltonians that realize non-Abelian chiral spin liquids on a kagome lattice.

Findings

Overlaps with model states exceed 0.9 for 12-site systems

Overlaps exceed 0.8 for 18-site systems

Hamiltonians exhibit non-Abelian topological order

Abstract

We search for short-range Hamiltonians of finite spin-1 kagome systems, maximizing the overlaps with lattice Moore-Read states. Our starting point is an exact, long-range parent Hamiltonian for such a state on a finite plane, obtained from conformal field theory. A truncation procedure is applied to it, which retains only short-range terms and makes it easy to define the Hamiltonian on a torus. Finally, the remaining coefficients are optimized, to yield maximized overlaps between exact diagonalization results and model ground states. In the best cases, these overlaps exceed 0.9 and 0.8 for the three lowest states of 12- and 18-site systems, respectively, suggesting that the obtained Hamiltonians are good parent Hamiltonians for a non-Abelian topological order.