Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy and Full Counting Statistics

Abstract: We consider the symmetry-resolved R\'{e}nyi and entanglement entropies for two-dimensional conformal field theories on a circle at nonzero temperature. We assume a unique ground state with a nonzero mass gap induced by the system's finite size and then calculate the leading corrections to the contributions of individual charge sectors in a low-temperature expansion. Besides the size of the mass gap and the degeneracy of the first excited state, these universal corrections depend only on the four-point correlation function of the primary fields. We also obtain thermal corrections to the full counting statistics of the ground state and define the \textit{probability fluctuations} function. It scales as $e^{-2 \pi \Delta_{\psi} \beta /L}$, where $\Delta_{\psi}$ is the scaling dimension of the lowest weight states. As an example, we explicitly evaluate the thermal corrections to the symmetry-resolved entanglement entropy and FCS for the spinless fermions.