Fermionic observables in the transverse Ising chain

TL;DR

This paper introduces s-holomorphic observables for the critical transverse-field Ising model, using complex-plane graphical representations, extending concepts from FK-Ising and spin-Ising models to quantum spin systems.

Contribution

It defines novel s-holomorphic observables for quantum spin chains, bridging classical and quantum models through complex analysis techniques.

Findings

Defined s-holomorphic observables for the quantum Ising chain

Connected these observables to classical FK and spin-Ising models

Discussed potential scaling limits of the observables

Abstract

We introduce a notion of s-holomorphicity suitable for certain quantum spin systems in one dimension, and define two observables in the critical transverse-field Ising model which have this property. The observables are defined using graphical representations in the complex plane, and are analogous to Smirnov's FK-Ising and spin-Ising observables, respectively. We also briefly discuss scaling-limits of these observables.