Non-invertible defects in generalized Ising models via strange correlator

TL;DR

This paper introduces a systematic method to construct Kramers-Wannier duality defects in generalized Ising models using the strange correlator, expanding understanding of non-invertible defects in statistical and gauge theories.

Contribution

It provides a new framework employing the strange correlator to realize KW duality defects across a broad class of models within the chain complex framework.

Findings

Constructed KW duality defects using strange correlator.

Extended duality defect analysis to generalized models.

Unified approach applicable to various topological models.

Abstract

Defects associated with non-invertible symmetries have attracted significant attention in recent years. Among them, Kramers-Wannier (KW) duality defects have been investigated in both classical statistical systems and quantum Hamiltonian models. Aasen et al. analyzed duality defects in the 2D Ising model and in statistical models built from fusion categories, while Koide et al. later constructed a duality defect in 4D lattice gauge theory. In this work, we extend these developments by providing a systematic construction of KW duality defects/KW defects for a broad class of models formulated within the chain complex framework. Our construction employs the strange correlator, an overlap between a topologically ordered state and a product state, to realize these KW defects.