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Real-time scattering in ϕ4 theory using matrix product states

Bahaa Al Sayegh1,* and Wissam Chemissany2,3,†

  • *Contact author: alsayeghbahaa@gmail.com
  • †Contact author: wchem@sas.upenn.edu
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Phys. Rev. Research 8, 023110 – Published 4 May, 2026

DOI: https://doi.org/10.1103/5v2j-12ps

Abstract

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 (uMPS) and the time-dependent variational principle (TDVP). A finite-entanglement scaling analysis at λ=0.8 bounds the critical mass-squared to μc2∈]−0.2595,−0.2594[ and provides a quantitative map of the symmetric, near-critical, and spontaneously 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) using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase (P11→11≃0.712, Δt≃−158 for μ2=+0.2) and almost perfectly elastic collisions in the spontaneously broken phase (P11→11≃1, Δt≃−108 for μ2=−0.1 and P11→11≃1, Δt≃−177.781 for μ2=−0.5). Crucially, the scattering protocol exhibits a distinctive divergence near the critical coupling; we show that this behavior serves as a dynamical signature of the quantum critical point, arising directly from the closing of the mass gap. These results demonstrate that TDVP-based uMPS can effectively probe nonperturbative scattering and critical dynamics in lattice field theories with controlled entanglement truncation.

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Phys. Rev. Research 8, 023110– Published 4 May, 2026
  • Received 24 November 2025
  • Accepted 17 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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