Extracting quantum field theory dynamics from an approximate ground state

• URL: http://arxiv.org/abs/2512.19594v1
• Date: Mon, 22 Dec 2025 17:25:24 GMT
• Title: Extracting quantum field theory dynamics from an approximate ground state
• Authors: Sophie Mutzel, Antoine Tilloy,
• Abstract summary: We develop a linear-programming method to extract information from static ground-state correlators in quantum field theory.<n>We test the method on the $1+1$-dimensional $4$ model, using a variational approximation to the vacuum.<n>The resulting mass gaps agree with renormalized Hamiltonian truncation and Borel-resummed perturbation theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a linear-programming method to extract dynamical information from static ground-state correlators in quantum field theory. We recast the Källén-Lehmann inversion as a convex optimization problem, in a spirit similar to the recent approach of Lawrence [arXiv:2408.11766]. This produces robust estimates of the smeared spectral density, the real-time propagator, and the mass gap directly from an approximate equal-time two-point function, and simultaneously yields an \emph{a posteriori} lower bound on the correlation-function error. We test the method on the $1+1$-dimensional $φ^4$ model, using a variational approximation to the vacuum -- relativistic continuous matrix product states -- that provides accurate correlators in the continuum and thermodynamic limits. The resulting mass gaps agree with renormalized Hamiltonian truncation and Borel-resummed perturbation theory across a wide range of couplings, demonstrating that accurate dynamical data can be recovered from a single equal-time slice.

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