Entanglement entropy in the Ising model with topological defects

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.

5 pages, 4 figures (updated published version)

References in corpus (4)

• Duality and defects in rational conformal field theory
• Entanglement through conformal interfaces
• Solution of the fermionic entanglement problem with interface defects
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories

Cited by in corpus (29)

• Nonlocality and entanglement in measured critical quantum Ising chains
• Domain wall melting across a defect
• Entanglement entropy and negativity in the Ising model with defects
• Rényi entropy and negativity for massless Dirac fermions at conformal interfaces and junctions
• Entanglement evolution after a global quench across a conformal defect
• Charge-resolved entanglement in the presence of topological defects
• Topological Defects in Floquet Circuits
• Universal entanglement signatures of interface conformal field theories
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions
• Fermionic Magic Resources of Quantum Many-Body Systems
• Zero-mode entanglement across a conformal defect
• Quantum Electronic Circuits for Multicritical Ising Models
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Dynamical quantum phase transitions from random matrix theory
• Duality defect in a deformed transverse-field Ising model
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
• Replicated Entanglement Negativity for Disjoint Intervals in the Ising and Free Compact Boson Conformal Field Theories
• Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state
• Isolated zero mode in a quantum computer from a duality twist
• Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias
• Probing Defects with Quantum Simulator Snapshots
• Entanglement flow in the Kane-Fisher quantum impurity problem
• Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization
• Boundary Conditions for the Entanglement Cut in 2D Conformal Field Theories
• Ballistic Entanglement Cloud after a Boundary Quench
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain
• Boundary critical phenomena in the quantum Ashkin-Teller model