Lattice study of the Silver Blaze phenomenon for a charged scalar ϕ4 field

We analyze a complex scalar field with ϕ4 interaction and a chemical potential μ on the lattice. An exact flux representation of the partition sum is used which avoids the complex action problem and based on a generalized worm algorithm we can run Monte Carlo simulations at arbitrary densities. We study thermodynamical quantities as a function of the chemical potential μ for zero and finite temperature. It is shown that at zero temperature thermodynamical observables are independent of μ up to a critical value μc (Silver Blaze phenomenon). In a spectroscopy calculation we cross-check that μc agrees with the mass m of the scalar field. The Silver Blaze region ends in a second order phase transition and we show that for low temperatures the second order phase boundary persists and separates a pseudo Silver Blaze region from a condensed phase with strong μ-dependence.