# Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor

## TL;DR

This study uses advanced quantum Monte Carlo simulations to explore the dynamic properties of large-flavor compact QED in (2+1)D, revealing phase transitions and spectral features that support the existence of a U(1) spin liquid and shed light on the phase transition's universality class.

## Contribution

It provides the first detailed numerical investigation of the dynamical behaviors across the deconfinement-to-confinement transition at large fermion flavor in compact QED.

## Key findings

- Identification of continua in spectral functions in the deconfined phase.
- Observation of gapped spectra and translational symmetry breaking in the confined phase.
- Evidence supporting the U(1) deconfined phase and insights into the phase transition nature.

## Abstract

Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor ($N_f$) and the strength of gauge fluctuations is mapped out~\cite{Xiao2018Monte}. Here we focus on the large fermion flavor case ($N_f=8$) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED$_3$-Gross-Neveu chiral O(2) universality whose properties still largely unknown.