Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study

TL;DR

This paper investigates low-energy bound states in two-dimensional spin systems near the Ising limit using a refined perturbative approach, revealing insights into their properties and excitations in the transverse-field Ising and XXZ models.

Contribution

It introduces an optimized perturbative continuous unitary transformation method to study bound states in 2D spin models near the Ising limit.

Findings

Bound states analyzed in the transverse-field Ising model and XXZ model.

Perturbative expansion about the Ising limit elucidates magnon behavior.

Connection established between the Ising model and the toric code in a magnetic field.

Abstract

We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.