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

Abstract

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 \textit{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.

Figures (7)

• Figure 1: Spectral function in the vacuum in the pseudoscalar (P) and scalar (S) sectors. Energies of the first few excited states are shown in dotted lines with blue color for negative (P) and red color for positive (S) ${\cal C}$-parity. The corresponding energy levels are presented in Table \ref{['tab:spectrum']}. The parameters of the system are $m/g=0.5, N=12, ga=0.5, \epsilon a = 0.02$. Energy is measured in the units of the first excited state energy that corresponds to the mass of the pseudoscalar meson $m_P$.
• Figure 2: Spectral function at zero and finite temperature for the pseudoscalar and scalar operators, with three values of the fermion mass compared. In all cases, $N=12, ga=0.5, \epsilon a = 0.02$.
• Figure 3: Frequency (upper panel) and width (lower panel) of the pseudoscalar and scalar meson peaks in the corresponding spectral functions, as functions of temperature. Thermal modifications broaden both peaks but leave the meson mass intact. Here we considered the same set conditions as in Fig. \ref{['fig:therm_spectr_func']} with $m/g=0.5$.
• Figure 4: Energy (top panel) and momentum (bottom panel) densities as functions of space and time for a strong quench in the vacuum ($T=0$, left panel) and at finite temperature ($T=2m_P$, right panel).
• Figure 5: Energy-energy correlator for a strong quench in the vacuum (left panel) and at finite $T$ (right panel).