Linear independence of nearest neighbor valence bond states on the kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state

TL;DR

This paper proves the linear independence of nearest neighbor valence bond states on the kagome lattice and constructs SU(2)-invariant Hamiltonians with a quantum spin liquid ground state, advancing understanding of topological quantum phases.

Contribution

It establishes the linear independence of valence bond states on large kagome lattices and constructs Hamiltonians with topologically degenerate ground states describing a Z2 spin liquid.

Findings

Linear independence of valence bond states on large kagome lattices.

Construction of Hamiltonians with SRK wavefunctions as ground states.

Evidence for a gapped Z2 spin liquid phase.

Abstract

A class of local SU(2)-invariant spin-1/2 Hamiltonians is studied that has ground states within the space of nearest neighbor valence bond states on the kagome lattice. Cases include "generalized Klein'' models without obvious non-valence bond ground states, as well as a "resonating-valence-bond" Hamiltonian whose unique ground states within the nearest neighbor valence bond space are four topologically degenerate "Sutherland-Rokhsar-Kivelson'' (SRK) type wavefunctions, which are expected to describe a gapped $\mathbb{Z}_2$ spin liquid. The proof of this uniqueness is intimately related to the linear independence of the nearest neighbor valence bond states on quite general and arbitrarily large kagome lattices, which is also established in this work. It is argued that the SRK ground states are also unique within the entire Hilbert space, depending on properties of the generalized Klein models. Applications of the strategies developed in this work to other lattice types are also discussed.