Extracting quantum field theory dynamics from an approximate ground state

TL;DR

This paper introduces a linear-programming approach to extract real-time dynamical information from static ground-state correlators in quantum field theory, enabling the estimation of spectral densities and mass gaps from a single time slice.

Contribution

It recasts the Källén-Lehmann inversion as a convex optimization problem, providing a robust method to derive dynamical quantities from static correlators in quantum field theory.

Findings

Accurately estimates mass gaps consistent with other methods.

Successfully recovers dynamical data from a single equal-time correlator.

Demonstrates applicability to the 1+1D φ^4 model across various couplings.

Abstract

We develop a linear-programming method to extract dynamical information from static ground-state correlators in quantum field theory. We recast the K\"all\'en-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 $\phi^4$ 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.