Tree-Graph Based Construction of Quantum Spin Models with Exact Ground State

Abstract

We propose a protocol to generate an antiferromagnetic S=1/2 Heisenberg model with the exact ground state based on a tree graph. The generated model has a correspondence with a tree graph and possesses the product state of singlet dimers as its unique ground state. A procedure for constructing a model with exact, massively degenerate ground states is also introduced.

v2: 5 pages, 5 figures, accepted version, v3: The same as v2, but with a correction to add the missing Fig.2