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

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 $(τ,m)$ 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 $τ$ as the lattice spacing goes to zero, with current data favoring $τ_* \approx 3.1$, 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.

Figures (3)

• Figure 1: Representative exact-diagonalization diagnostics of the expansion-driven sweep.(a) Instantaneous gap landscape $\Delta(\tau,m)$ with pseudo-critical line $m_{\mathrm{c}}(\tau)=\mathop{\mathrm{arg\,min}}\limits_m\Delta(\tau,m)$ (white). Dashed lines indicate a representative crossing point $(\tau_c,m_\ast)$. (b) Non-adiabaticity $1-F_{\rm GS}(\tau)$ for several curvature radii $L$ at fixed $m_\ast$. (c) Excitation energy density $\epsilon_{\rm exc}(\tau)$ for the same parameters. (d) Structure-factor response $\Delta S_q(k,\tau)$ and a check of the redshift law $p_{\rm peak}(\tau)\simeq\pi/a(\tau)$ in the inset. The data illustrate how the expansion-induced deformation of the spectrum translates into loss of adiabatic following, energy injection, and a physically redshifted response. $N=14$ is used for exact diagonalization. Panel (a) is intentionally shown at fixed small $N$ to display the full gap landscape; the fate of the late-time dip under $\ell_{\rm phys}\to\infty$ at fixed $a_{\rm latt}$ and under subsequent continuum extrapolation is analyzed separately in Fig. \ref{['fig:largeN_fixedmass']}.
• Figure 2: Fixed-cutoff thermodynamic limit and continuum drift from matrix-product states.(a) Largest-volume gap traces $\Delta(\tau)$ at $\ell_{\rm phys}=48$ for $a_{\rm latt}=1.0,0.8,0.6,0.48$, with markers at the refined dip times. (b) Fixed-cutoff thermodynamic extrapolation of $\tau_\ast(a_{\rm latt},\ell_{\rm phys})$ versus $1/\ell_{\rm phys}$ for the same four branches. The common physical-length ladder is $\ell_{\rm phys}\approx 16,24,32,40,48$. (c) Continuum drift of the thermodynamic dip time $\tau_\ast^{(\infty)}(a_{\rm latt})$. The solid line is the fit linear in $a_{\rm latt}$, giving $\tau_\ast^{(\infty,0)}\approx 3.12$, while the dashed line is the $a_{\rm latt}^2$ check, giving $2.63$. The shadow indicates fitting errors. (d) Thermodynamic-limit dip depth $\Delta_\ast^{(\infty)}(a_{\rm latt})$, shown only as a diagnostic. The dip time survives the fixed-cutoff thermodynamic limit and drifts to later times as the continuum is approached, while the dip depth itself remains less regular. Error bars in (d) denote numerical and extrapolation uncertainties rather than statistical sampling errors. Error bars in the other panels are not shown because they are negligible. For each fixed $a_{\rm latt}$, the uncertainty of $\Delta_{\ast}$ is estimated from the difference between the refined and coarse dip-depth extractions, with a small positive floor to avoid spuriously vanishing bars. These pointwise uncertainties are then propagated through the thermodynamic extrapolation in $1/\ell_{\rm phys}$, and the final error bar on $\Delta_{\ast}^{(\infty)}(a_{\rm latt})$ is obtained by combining in quadrature the weighted-fit intercept error and a model-spread estimate given by one half of the difference between the linear and quadratic extrapolated intercepts.
• Figure 3: Operational irreversibility front and its LOCC signatures.(a) Smoothed entropy-production landscape $\widetilde{\Sigma}(\tau,m)$ at $\beta=10$ for a representative $N=10$ run. The white curve is the pseudo-critical line $m_{\mathrm{c}}(\tau)$ and the orange curve is the extracted operational front $m_{\mathrm{DPT}}(\tau,\beta=10)$. (b) Temperature dependence of the extracted front for $\beta=0.5,1,2,5,10$ and $m_{\mathrm{c}}(\tau)$. (c) Front width after onset, showing systematic sharpening at larger $\beta$. The colors correspond to the temperatures shown in panel (b). (d) Comparison between the full front and two LOCC reconstructions for end blocks of fixed size. (e) Finite-size sharpening of the front at low temperature: the mean width and the mean offset to $m_{\mathrm{c}}(\tau)$ decrease, while the fit-based sharpness increases with $N$. (f) Error to the full front versus LOCC block size $\ell$, showing that tomography-based LOCC outperforms direct local measurement and that both improve with local access.