Grand Canonical Ensembles, Multiparticle Wave Functions, Scattering Data, and Lattice Field Theories

We show that information about scattering data of a quantum field theory can be obtained from studying the system at finite density and low temperatures. In particular we consider models formulated on the lattice that can be exactly dualized to theories of conserved charge fluxes on lattice links. Apart from eliminating the complex action problem at nonzero chemical potential μ, these dualizations allow for a particle world line interpretation of the dual fluxes from which one can extract data about the two-particle wave function. As an example we perform dual Monte Carlo simulations of the two-dimensional O(3) model at nonzero μ and finite volume, whose nonperturbative spectrum consists of a massive triplet of particles. At nonzero μ particles are induced in the system, which at sufficiently low temperature give rise to sectors of fixed particle number. We show that the scattering phase shifts can be obtained either from the critical chemical potential values separating the sectors or directly from the wave function in the two-particle sector. We find that both methods give excellent agreement with the exact result. We discuss the applicability and generality of the new approaches.