Entanglement entropy in the Ising model with topological defects

TL;DR

This paper presents a lattice-based analysis of entanglement entropy in the Ising model with topological defects, revealing finite-size effects and zero-energy mode contributions that differ from field-theoretic predictions.

Contribution

It provides the first ab-initio lattice computation of EE in the presence of topological defects, highlighting the role of zero-energy modes in universal subleading terms.

Findings

Zero-energy modes cause significant finite-size corrections.

Universal subleading EE term is due to zero-energy modes, not the modular S-matrix.

Behavior of EE depends on subsystem geometry relative to the defect.

Abstract

Entanglement entropy~(EE) contains signatures of many universal properties of conformal field theories~(CFTs), especially in the presence of boundaries or defects. In particular, {\it topological} defects are interesting since they reflect internal symmetries of the CFT, and have been extensively analyzed with field-theoretic techniques with striking predictions. So far, however, very few ab-initio, lattice computations of these predictions have been available. Here, we present an ab-initio analysis of EE for the Ising model in the presence of a topological defect. While the behavior of the EE depends, as expected, on the geometric arrangement of the subsystem with respect to the defect, we find that zero-energy modes give rise to crucial finite-size corrections. Importantly, contrary to the field-theory predictions, the universal subleading term in the EE when the defect lies at the edge of the subsystem arises entirely due to these zero-energy modes and is not directly related to the modular S-matrix of the Ising CFT.