Using approximate renormalization group methods, the authors map phase diagrams of Z3 spin and gauge models and find that only chiral spin models and their duals show an infinite Devil's flower family of inhomogeneous phases, while different RG schemes disagree on the number of phases.
Finite-density QCD, $\mathcal{PT}$ symmetry, and dual algorithms
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abstract
Finite-density QCD and many other field theories with sign problems have a $\mathcal{PT}$-type symmetry. After a brief introduction to $\mathcal{PT}$-symmetric field theories, a real dual representation for $\mathcal{PT}$-symmetric scalar field theories with complex actions is derived. We show that $\mathcal{PT}$-symmetric field theories can exhibit exotic behavior, including sinusoidally modulated propagators, disorder lines, and spatially inhomogeneous pattern-forming phases. We discuss the interplay of duality, $\mathcal{PT}$-symmetry and pattern formation using a $\phi^4$ model and $Z(N)$ spin model with sign problems as examples. These behaviors may occur in finite-density QCD and related models.
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Exotic phases in finite-density $\mathbb{Z}_3$ theories
Using approximate renormalization group methods, the authors map phase diagrams of Z3 spin and gauge models and find that only chiral spin models and their duals show an infinite Devil's flower family of inhomogeneous phases, while different RG schemes disagree on the number of phases.