Spin Hamiltonians with resonating-valence-bond ground states

TL;DR

This paper constructs SU(2)-invariant spin-1/2 Hamiltonians with resonating-valence-bond ground states, overcoming the challenge of non-orthogonal dimer configurations, and explores their potential quantum criticality.

Contribution

It introduces a method to realize RVB ground states in spin-1/2 Hamiltonians while addressing the non-orthogonality of dimer configurations, advancing understanding of quantum critical points.

Findings

Hamiltonians with RVB ground states constructed

Dependence of physics on dimer-spin relations analyzed

Potential for quantum critical behavior identified

Abstract

Quantum dimer models exhibit quantum critical points and liquid states when the ground state is the resonating-valence bond (RVB) state. We construct SU(2)-invariant spin-1/2 Hamiltonians with the same RVB ground state. The main technical obstacle overcome is the fact that different "dimer" configurations in the spin model are not orthogonal to each other. We show that the physics depends on how dimers are related to the spins, and find a Hamiltonian that may be quantum critical.