Eigenvector Continuation for Resonance States*

Eigenvector continuation (EC) has emerged as an intriguing method to yield approximate solutions for computationally expensive eigenvalue problems with great speed and accuracy. With EC, the essence of a quantum system is "learned" through the construction of a highly effective (non-orthogonal) basis, leading to a variational calculation of the states of interest with rapid convergence. Extracting resonance energies of few-body systems is of great importance in nuclear physics, but it continues to pose challenges due to the large computational complexity involved. In this work we study EC as an option to facilitate such calculations. To that end, we use both finite-volume techniques, where resonances are manifest as avoided crossings of energy levels, as well as direct studies in momentum space, where resonances can be identified after analytic continuation of the Schrödinger equation. In both cases we find that EC makes it possible to extrapolate trajectories of resonance states. In particular, we discuss the possibility of predicting resonances based on bound training states alone, tracing their transition into the continuum as a parameter in the Hamiltonian is varied.