Entanglement-spectrum fingerprint of a non-invertible symmetry: the Kramers--Wannier duality defect on the lattice

Abstract

Non-invertible symmetries are characterized by topological defects of irrational quantum dimension, but their imprint on the entanglement of a quantum many-body state has not been resolved at the level of the spectrum. We show that the categorical data of the canonical example -- the Kramers--Wannier (KW) duality defect of the critical Ising chain, with quantum dimension d_sigma=sqrt(2) -- is encoded in the single-particle entanglement spectrum of its ground state: a maximally mixed Majorana zero mode is the spectral origin of the boundary entropy log g=(1/2)log 2, hence of d_sigma itself. Reading the same duality-twisted ground state along two independent routes -- the transfer-matrix momentum shift and the Casimir curvature of the energy -- pins the twist-field weight h_sigma=1/16 twice over, and the defect Hilbert space organizes into a half-integer sigma-twisted conformal tower. This promotes the boundary entropy from an integrated number to a level-resolved spectral signature of non-invertibility, and supplies an exactly solvable calibration target for tensor-network studies of duality defects that lack a free-fermion shortcut.