Algebraic-Dynamical Theory for Quantum Spin-1/2: the Two-spin limit and Implications for Lattice Models

TL;DR

This paper develops an algebraic-dynamical framework for strongly interacting quantum spin-1/2 systems, demonstrating its effectiveness through exact solutions and perturbation theory, with implications for lattice models.

Contribution

It introduces a systematic algebraic-dynamical approach for quantum spin models, including exact solutions and perturbation methods, advancing understanding of strongly interacting systems.

Findings

Exact solutions for two-spin problems using ADT

Successful perturbation calculations matching known ground states

Implications for modeling lattice quantum spin systems

Abstract

Recently, an {\it algebraic-dynamical theory} (ADT) for strongly interacting many-body quantum Hamiltonians in W. Ding, arXiv: 2202.12082 (2022). By introducing the complete operator basis set, ADT proposes a generic framework for systematically constructing dynamical theories for interacting quantum Hamiltonians, using quantum entanglement as the organizing principle. In this work, we study exact ADT solutions of interacting two-spin problems which can be used as "free theories" for perturbation study on relevant solvable limits. Then we perform ADT perturbation calculations and obtain the correct ground state under the perturbation, which shows that the ADT framework is capable of constructing correct dynamical perturbation theories for strongly interacting quantum spin models. We also discuss the implication for relevant lattice models.