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

Details 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 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

2009-06-02

arxiv.org/abs/0906.0357v2

Phys. Rev. B 80, 165131 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

published version, many references added, some typos corrected

Scientific paper

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.

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