2025/11/19 by Sayegh, Bahaa Al, Chemissany, Wissam
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2511.15697
We investigate the critical behavior and real-time scattering dynamics of the interacting ϕ4 quantum field theory in (1+1) dimensions using uniform matrix product states and the time-dependent variational principle. A finite-entanglement scaling analysis at λ= 0.8 bounds the critical mass-squared to μc2 ∈ [-0.3190,-0.3185] and provides a quantitative map of the symmetric, near-critical, weakly broken, and deeply broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability P11→ 11(E) and Wigner time delay Δt(E) following the prescription of Jha et al. [Phys. Rev. Research 7, 023266 (2025)]. We find strongly inelastic scattering in the symmetric phase (P11→ 11 ≃ 0.63, Δt ≃ -180 for μ2 = 0.2), almost perfectly elastic collisions in the spontaneously broken phase (P11→ 11 ≃ 0.998, Δt ≃ -270 for μ2=-0.2 and P11→ 11 ≃ 1, Δt ≃ -177.781 for μ2=-0.5), and a breakdown of the sandwich evolution precisely at the critical coupling, which provides a dynamical signature of the quantum critical point. These results demonstrate that TDVP-based uniform matrix product states can probe nonperturbative scattering and critical dynamics in lattice ϕ4 theory with controlled entanglement truncation.