Multi-Particle Spectral Properties in the Transverse Field Ising Model by Continuous Unitary Transformations

TL;DR

This paper solves the one-dimensional transverse field Ising model using continuous unitary transformations, achieving high accuracy in spectral properties by exploiting algebraic closure related to fermionic mappings, and computes multi-particle excitation contributions.

Contribution

It introduces a method to analyze spectral properties of the transverse field Ising model without relying on Jordan-Wigner transformation, addressing multi-particle excitations analytically.

Findings

Accurate spectral calculations in high-field limit

Analytical expressions for multi-particle contributions

Extension to three-particle excitations near criticality

Abstract

The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The closure is related to the possibility to map the model by Jordan-Wigner transformation to non-interacting fermions. But it is proven without referring to this mapping. The effective model derived by the continuous unitary transformations is used to compute the contributions of one, two, and three elementary excitations to the diagonal dynamic structure factors. The three-particle contributions have so far not been addressed analytically, except close to the quantum critical point.