Exotic phases in finite-density ℤ 3 theories
Abstract Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and CK $$ \mathcal{CK} $$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which a...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2025)077 |
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| Summary: | Abstract Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and CK $$ \mathcal{CK} $$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ 3 models in dimensions one through four. Chiral ℤ 3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ 3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ N models, SU(N) models and nonzero temperature. |
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| ISSN: | 1029-8479 |