Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit

TL;DR

This paper investigates the critical behavior of quantum magnets with long-range interactions using high-order linked-cluster expansions, revealing insights into quasiparticle properties and quantum-critical regimes.

Contribution

It introduces a novel approach using perturbative continuous unitary transformations on white graphs to treat long-range interactions in quantum many-body systems.

Findings

Determined quasiparticle gaps for the long-range transverse-field Ising chain.

Accessed quantum-critical regimes including critical exponents.

Analyzed both ferro- and antiferromagnetic cases with logarithmic corrections.

Abstract

Quasiparticle properties of quantum magnets with long-range interactions are investigated by high-order linked-cluster expansions in the thermodynamic limit. It is established that perturbative continuous unitary transformations on white graphs are a promising and flexible approach to treat long-range interactions in quantum many-body systems. We exemplify this scheme for the one-dimensional transverse-field Ising chain with long-range interactions. For this model the elementary Quasiparticle gap is determined allowing to access the quantum-critical regime including critical exponents and multiplicative logarithmic corrections for the ferro- and antiferromagnetic case.