Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas

We analyze 2-point functions in the relativistic Bose gas on the lattice, i.e., a charged scalar ϕ⁴ field with chemical potential μ. Using a generalized worm algorithm we perform a Monte Carlo simulation in a dual representation in terms of fluxes where the complex action problem is overcome. We explore various aspects of lattice spectroscopy at finite density and zero temperature, such as the asymmetry of forward and backward propagation in time and the transition into the condensed phase. It is shown that after a suitable subtraction the exponents for forward and backward propagation are independent of μ and agree with the mass obtained from the propagator at μ=0. This holds for μ<μ_c and shows that below the condensation transition the mass is independent of μ as expected from the Silver Blaze scenario