Reflected entropy, symmetries and free fermions

• Autores: Bueno, Pablo; Casini, Horacio German
• Año de publicación: 2020
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: CONFORMAL FIELD THEORY; GLOBAL SYMMETRIES
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

Exploiting the split property of quantum field theories (QFTs), a notion of von Neumann entropy associated to pairs of spatial subregions has been recently proposed both in the holographic context — where it has been argued to be related to the entanglement wedge cross section — and for general QFTs. We argue that the definition of this “reflected entropy” can be canonically generalized in a way which is particularly suitable for orbifold theories — those obtained by restricting the full algebra of operators to those which are neutral under a global symmetry group. This turns out to be given by the full-theory reflected entropy minus an entropy associated to the expectation value of the “twist” operator implementing the symmetry operation. Then we show that the reflected entropy for Gaussian fermion systems can be simply written in terms of correlation functions and we evaluate it numerically for two intervals in the case of a two-dimensional Dirac field as a function of the conformal cross-ratio. Finally, we explain how the aforementioned twist operators can be constructed and we compute the corresponding expectation value and reflected entropy numerically in the case of the ℤ2 bosonic subalgebra of the Dirac field.
Fil: Bueno, Pablo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina