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

TL;DR

This paper constructs and analyzes a family of SU(2)-invariant spin-1/2 Hamiltonians that can realize various valence bond and RVB phases, including Z2 and U(1) spin liquids, on different lattices.

Contribution

It introduces a controlled perturbation method to realize and study different RVB phases in SU(2)-invariant Hamiltonians on various lattices.

Findings

Realization of Z2 RVB phases in 2D.

Existence of U(1) RVB phases with gapless photons in 3D.

Construction of models on pyrochlore lattice with Z2 and U(1) RVB phases.

Abstract

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.