Symmetry-resolved modular correlation functions in free fermionic theories

Fuente: arXiv
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Autores principales: Di Giulio, Giuseppe, Erdmenger, Johanna
Formato: Preprint
Publicado: 2023
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author Di Giulio, Giuseppe
Erdmenger, Johanna
author_facet Di Giulio, Giuseppe
Erdmenger, Johanna
contents As a new ingredient for analyzing the fine structure of entanglement, we study the symmetry resolution of the modular flow of $U(1)$-invariant operators in theories endowed with a global $U(1)$ symmetry. We provide a consistent definition of symmetry-resolved modular flow that is defined for a local algebra of operators associated to a sector with fixed charge. We also discuss the symmetry-resolved modular correlation functions and show that they satisfy the KMS condition in each symmetry sector. Our analysis relies on the factorization of the Hilbert space associated to spatial subsystems. We provide a toolkit for computing the symmetry-resolved modular correlation function of the charge density operator in free fermionic theories. As an application, we compute this correlation function for a $1+1$-dimensional free massless Dirac field theory and find that it is independent of the charge sector at leading order in the ultraviolet cutoff expansion. This feature can be regarded as a charge equipartition of the modular correlation function. Although obtained for free fermions, these results may be of potential interest for bulk reconstruction in AdS/CFT.
format Preprint
id arxiv_https___arxiv_org_abs_2305_02343
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Symmetry-resolved modular correlation functions in free fermionic theories
Di Giulio, Giuseppe
Erdmenger, Johanna
High Energy Physics - Theory
Statistical Mechanics
As a new ingredient for analyzing the fine structure of entanglement, we study the symmetry resolution of the modular flow of $U(1)$-invariant operators in theories endowed with a global $U(1)$ symmetry. We provide a consistent definition of symmetry-resolved modular flow that is defined for a local algebra of operators associated to a sector with fixed charge. We also discuss the symmetry-resolved modular correlation functions and show that they satisfy the KMS condition in each symmetry sector. Our analysis relies on the factorization of the Hilbert space associated to spatial subsystems. We provide a toolkit for computing the symmetry-resolved modular correlation function of the charge density operator in free fermionic theories. As an application, we compute this correlation function for a $1+1$-dimensional free massless Dirac field theory and find that it is independent of the charge sector at leading order in the ultraviolet cutoff expansion. This feature can be regarded as a charge equipartition of the modular correlation function. Although obtained for free fermions, these results may be of potential interest for bulk reconstruction in AdS/CFT.
title Symmetry-resolved modular correlation functions in free fermionic theories
topic High Energy Physics - Theory
Statistical Mechanics
url https://arxiv.org/abs/2305.02343