Quantum Information Dynamics of QED$_2$ in Expanding de Sitter Universe

TL;DR

This paper investigates the dynamics of quantum electrodynamics in two dimensions within an expanding de Sitter universe, revealing how cosmological expansion influences quantum spectral properties and irreversibility.

Contribution

It introduces a detailed analysis of QED$_2$ in de Sitter space, identifying a pseudo-critical line that governs adiabaticity loss and spectral transitions, using exact diagonalization and matrix-product states.

Findings

A pseudo-critical line controls excitation growth and spectral shifts.

Late-time spectral dips persist in the infinite volume limit.

Irreversibility fronts are detectable via local operations and classical communication.

Abstract

We study QED$_2$ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as $1/a(t)$ while the electric term grows as $g^2 a(t)$, sweeping the spectrum through a moving narrow-gap region in the $(\tau,m)$ plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later $\tau$ as the lattice spacing goes to zero, with current data favoring $\tau_* \approx 3.1$, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED$_2$ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.