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A relativistic Bose gas at finite density suffers from a sign problem thatmakes direct numerical simulations not feasible. One possible solution to thesign problem is to re-express the path integral in terms of Lefschetz thimbles.Using this approach we study the relativistic Bose gas both in the symmetricphase (low-density) and the spontaneously broken phase (high-density). In thehigh-density phase we break explicitly the symmetry and determine thedependence of the order parameter on the breaking. We study the relativecontributions of the dominant and sub-dominant thimbles in this phase. We findthat the sub-dominant thimble only contributes substantially when the explicitsymmetry breaking is small, a regime that is dominated by finite volumeeffects. In the regime relevant for the thermodynamic limit, this contributionis negligible.

A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm