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, 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, no lattice computation of EE has been available. Here, we present an abinitio 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.
Highlights
Entanglement plays a central role in the development of long-range correlations in quantum critical phenomena
For zero-temperature ground states of 1 þ 1D quantum-critical systems described by conformal field theories (CFTs), the von Neumann entropy [equivalently, entanglement entropy (EE)] for a subsystem exhibits universal logarithmic scaling with the subsystem size [1,2]
After usual folding maneuvers, the subleading term can be equated to a boundary entropy with double the bulk degrees of freedom [16–18]
Summary
Entanglement entropy (EE) contains signatures of many universal properties of conformal field theories (CFTs), especially in the presence of boundaries or defects. For zero-temperature ground states of 1 þ 1D quantum-critical systems described by conformal field theories (CFTs), the von Neumann entropy [equivalently, entanglement entropy (EE)] for a subsystem exhibits universal logarithmic scaling with the subsystem size [1,2] The coefficient of this scaling determines a fundamental property of the bulk CFT: the central charge. These defects commute with the generators of conformal transformations and can be deformed without affecting the values of the correlation functions, as long as they are not taken across field insertions ( the moniker topological) They reflect the internal symmetries of the CFT and relate the order-disorder dualities of the CFT to the high-low temperature dualities of the corresponding offcritical model [10,13,14].
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