The Interface of the FK-representation of the Quantum Ising Model Converges to the $SLE_{16/3}$

TL;DR

This paper demonstrates that the interface in the FK-representation of the 1D quantum Ising model converges to the Schramm-Loewner Evolution with parameter 16/3, revealing a deep connection between quantum spin models and conformal invariance.

Contribution

It establishes the convergence of the FK interface in the 1D quantum Ising model to SLE_{16/3}, a significant step in understanding quantum models through conformal field theory.

Findings

FK interface converges to SLE_{16/3}

Results connect quantum Ising models with conformal invariance

Provides rigorous proof of interface scaling limit

Abstract

We study the interface in the FK-representation of the 1D quantum Ising model and show that in the limit, it converges to the $SLE_{16/3}$ curve.