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

Abstract

A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign 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 symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density phase we break explicitly the symmetry and determine the dependence of the order parameter on the breaking. We study the relative contributions of the dominant and sub-dominant thimbles in this phase. We find that the sub-dominant thimble only contributes substantially when the explicit symmetry breaking is small, a regime that is dominated by finite volume effects. In the regime relevant for the thermodynamic limit, this contribution is negligible.

12 pages, 6 figures, 1 table

References in corpus (5)

• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Monte Carlo study of real time dynamics
• Method for simulating O(N) lattice models at finite density
• Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles
• Extended Mean Field study of complex ${\varphi }^4$-theory at finite density and temperature

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