Real-time Scattering in ϕ^4 Theory using Matrix Product States
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| Format: | Preprint |
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2025
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| _version_ | 1866918452814413824 |
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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 |
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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 |