The density of states approach to dense quantum systems

Abstract

We develop a first-principle generalised density of state method for studying numerically quantum field theories with a complex action. As a proof of concept, we show that with our approach we can solve numerically the strong sign problem of the $Z_3$ spin model at finite density. Our results are confirmed by standard simulations of the theory dual to the considered model, which is free from a sign problem. Our method opens new perspectives on ab initio simulations of cold dense quantum systems, and in particular of Yang-Mills theories with matter at finite densities, for which Monte Carlo based importance sampling are unable to produce sufficiently accurate results.

4 pages, 3 figures

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• Canonical partition function and finite density phase transition in lattice QCD
• The density of states in gauge theories
• Method for simulating O(N) lattice models at finite density
• The QCD phase diagram according to the center group
• Critical Behavior of CP^1 at theta = pi, Haldane's Conjecture and the Universality Class
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