Real-time Scattering in ϕ^4 Theory using Matrix Product States

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Main Authors: Sayegh, Bahaa Al, Chemissany, Wissam
Format: Preprint
Published: 2025
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author Sayegh, Bahaa Al
Chemissany, Wissam
author_facet Sayegh, Bahaa Al
Chemissany, Wissam
contents We investigate the critical behavior and real-time scattering dynamics of the interacting $ϕ^4$ 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 $μ_c^2 \in ]-0.2595,-0.2594[$ 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 $P_{11\to 11}(E)$ and Wigner time delay $Δt(E)$ using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11} \simeq 0.712$, $Δt \simeq -158$ for $μ^2 = +0.2$) and almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11} \simeq 1$, $Δt \simeq -108$ for $μ^2=-0.1$ and $P_{11\to 11} \simeq 1$, $Δt \simeq -177.781$ for $μ^2=-0.5$). 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_15697
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Real-time Scattering in ϕ^4 Theory using Matrix Product States
Sayegh, Bahaa Al
Chemissany, Wissam
High Energy Physics - Theory
Strongly Correlated Electrons
High Energy Physics - Lattice
Quantum Physics
We investigate the critical behavior and real-time scattering dynamics of the interacting $ϕ^4$ 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 $μ_c^2 \in ]-0.2595,-0.2594[$ 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 $P_{11\to 11}(E)$ and Wigner time delay $Δt(E)$ using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11} \simeq 0.712$, $Δt \simeq -158$ for $μ^2 = +0.2$) and almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11} \simeq 1$, $Δt \simeq -108$ for $μ^2=-0.1$ and $P_{11\to 11} \simeq 1$, $Δt \simeq -177.781$ for $μ^2=-0.5$). 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.
title Real-time Scattering in ϕ^4 Theory using Matrix Product States
topic High Energy Physics - Theory
Strongly Correlated Electrons
High Energy Physics - Lattice
Quantum Physics
url https://arxiv.org/abs/2511.15697