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

TL;DR

This paper introduces a method to construct quantum spin models with exact ground states using tree graphs, enabling precise control over ground state properties and degeneracy in antiferromagnetic systems.

Contribution

It presents a novel protocol for designing quantum spin models with exact ground states based on tree graph structures, including models with highly degenerate ground states.

Findings

Successfully constructs models with exact ground states

Establishes correspondence between models and tree graphs

Provides a method for creating models with degenerate ground states

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.