Deconfinement from Thermal Tensor Networks: Universal CFT signature in (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theory
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arXiv
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| Format: | Preprint |
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2026
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| author | Naravane, Adwait Sugimoto, Yuto Akiyama, Shinichiro Haegeman, Jutho Ueda, Atsushi |
| author_facet | Naravane, Adwait Sugimoto, Yuto Akiyama, Shinichiro Haegeman, Jutho Ueda, Atsushi |
| contents | Tensor networks offer a sign-problem-free approach to study lattice gauge theories, but extracting precise universal information associated with the deconfinement transition remains challenging. In this work, we study the deconfinement transition of (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theories at finite temperature using a thermal tensor network approach, where the partition functions at finite temperature are formulated as three-dimensional tensor networks. These tensor networks are first contracted in the temporal direction, and the subsequent coarse-graining in the spatial directions yields a renormalized transfer matrix, the spectrum of which directly encodes the universal conformal field theory data. In particular, by numerically extracting the central charge and scaling dimensions, we verify that the universality class of the thermal deconfinement transition matches the prediction of the Svetitsky-Yaffe conjecture for $N=2,3,5$. Moreover, we show that the $\mathbb{Z}_5$ theory at finite temperature exhibits an intermediate phase with an emergent U(1) symmetry. Critical couplings are determined via Gu-Wen ratios and agree with existing Monte Carlo simulations. Finally, extrapolating these critical couplings at finite temperature enables us to determine the deconfinement transition points for $N=2,3$ at zero temperature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_13124 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deconfinement from Thermal Tensor Networks: Universal CFT signature in (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theory Naravane, Adwait Sugimoto, Yuto Akiyama, Shinichiro Haegeman, Jutho Ueda, Atsushi High Energy Physics - Theory Statistical Mechanics High Energy Physics - Lattice Tensor networks offer a sign-problem-free approach to study lattice gauge theories, but extracting precise universal information associated with the deconfinement transition remains challenging. In this work, we study the deconfinement transition of (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theories at finite temperature using a thermal tensor network approach, where the partition functions at finite temperature are formulated as three-dimensional tensor networks. These tensor networks are first contracted in the temporal direction, and the subsequent coarse-graining in the spatial directions yields a renormalized transfer matrix, the spectrum of which directly encodes the universal conformal field theory data. In particular, by numerically extracting the central charge and scaling dimensions, we verify that the universality class of the thermal deconfinement transition matches the prediction of the Svetitsky-Yaffe conjecture for $N=2,3,5$. Moreover, we show that the $\mathbb{Z}_5$ theory at finite temperature exhibits an intermediate phase with an emergent U(1) symmetry. Critical couplings are determined via Gu-Wen ratios and agree with existing Monte Carlo simulations. Finally, extrapolating these critical couplings at finite temperature enables us to determine the deconfinement transition points for $N=2,3$ at zero temperature. |
| title | Deconfinement from Thermal Tensor Networks: Universal CFT signature in (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theory |
| topic | High Energy Physics - Theory Statistical Mechanics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2602.13124 |