AG Mathematische Physik: Giuseppe Di Giulio (Uni Würzburg) Symmetry-resolved modular correlation functions in free fermionic theories

Giuseppe Di Giulio (Uni Würzburg)

Symmetry-resolved modular correlation functions in free fermionic theories

Abstract:
Recently there has been a huge research activity on the interplay between
symmetries and entanglement, exploiting the block-diagonal structure of the
reduced density matrix (RDM) in each charge sector. The goal of this talk is to
study how the presence of a global U(1) charge affects the modular flow, a
central object in the algebraic description of quantum field theory. Roughly
speaking, the modular flow is given by a generalized time evolution induced by a
RDM of a given spatial region. I will discuss the symmetry resolution of the
modular flow and the modular correlation function of U(1)-invariant operators. I
will provide a consistent definition of symmetry-resolved modular flow defined
for a local algebra of operators associated with a sector with a fixed charge. I
will also discuss the symmetry-resolved modular correlation functions, showing
that they satisfy the KMS condition in each symmetry sector. In order to
complement this analysis with an example, I will provide a toolkit for computing
the symmetry-resolved modular correlation function of the charge density
operator in free fermionic theories. I will show that, in a 1 + 1-dimensional
free massless Dirac field theory, this quantity is independent of the charge
sector at leading order in the ultraviolet cutoff expansion. This feature can be
regarded as an equipartition of the modular correlation function.