SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases

Details SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases

2005-02-05

arxiv.org/abs/cond-mat/0502146v2

Phys. Rev. B 72, 064413 (2005)

Physics

Condensed Matter

Strongly Correlated Electrons

16 pages, 15 figures; 1 figure and some references added; some minor typos fixed

Scientific paper

10.1103/PhysRevB.72.064413

We construct a family of rotationally invariant, local, S=1/2 Klein Hamiltonians on various lattices that exhibit ground state manifolds spanned by nearest-neighbor valence bond states. We show that with selected perturbations such models can be driven into phases modeled by well understood quantum dimer models on the corresponding lattices. Specifically, we show that the perturbation procedure is arbitrarily well controlled by a new parameter which is the extent of decoration of the reference lattice. This strategy leads to Hamiltonians that exhibit i) $Z_2$ RVB phases in two dimensions, ii) U(1) RVB phases with a gapless ``photon'' in three dimensions, and iii) a Cantor deconfined region in two dimensions. We also construct two models on the pyrochlore lattice, one model exhibiting a $Z_2$ RVB phase and the other a U(1) RVB phase.

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