Thermal modifications of mesons and energy-energy correlators from real-time simulations of a $U(1)$ lattice gauge theory

We investigate thermal properties of a $U(1)$ lattice gauge theory in $1+1$-dimensions through real-time simulations. We extract the spectral functions directly coupling to the pseudoscalar and scalar mesons, demonstrating the thermal modifications of these states with increasing temperatures. Introducing the notion of energy-flow operators, we quantify the temporal build-up of correlations in the energy flows across the lattice. We demonstrate that energy-energy correlators fail to factorize to products of energy flows, both in the vacuum and at nonzero-temperature, indicating the presence of non-trivial correlations in the quantum states. Our results constitute a first real-time ab-initio study of bound state thermal broadening and finite temperature energy-flow correlations in a gauge theory, providing a benchmark for future studies of hadronic matter under extreme conditions.