Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities

TL;DR

This paper presents an algebraic approach based on bond algebras to construct and solve exactly solvable Hamiltonians, with applications to topological quantum models like Kitaev's toric code and honeycomb models.

Contribution

It introduces a novel algebraic methodology using bond operators for designing and solving exactly solvable Hamiltonians in complex quantum systems.

Findings

Successfully applied to Kitaev's models and others

Provides a systematic way to analyze topological quantum order

Enables exact solutions for complex lattice models

Abstract

We introduce an algebraic methodology for designing exactly-solvable Lie model Hamiltonians. The idea consists in looking at the algebra generated by bond operators. We illustrate how this method can be applied to solve numerous problems of current interest in the context of topological quantum order. These include Kitaev's toric code and honeycomb models, a vector exchange model, and a Clifford gamma model on a triangular lattice.