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arXiv · 2603.02739

Tensor renormalization group approach to the $O(2)$ models via symmetry-twisted partition functions

Shinichiro Akiyama·Raghav G. Jha·Jun Maeda·Yuya Tanizaki·Judah Unmuth-Yockey
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Abstract

We investigate critical phenomena in the $O(2)$ models using symmetry-twisted partition functions that can be efficiently computed within the tensor renormalization group framework. We first demonstrate, taking the three-dimensional model as an example, that symmetry-twisted partition functions detect the spontaneous breaking of global continuous symmetry. We then consider the same model in two dimensions, where the Berezinskii--Kosterlitz--Thouless (BKT) transition occurs. Since symmetry-twisted partition functions directly provide the helicity modulus at a finite twist angle, we determine the BKT transition point. These results are presented based on Ref.~\cite{Akiyama:2026dzg}. Finally, in addition to the original paper~\cite{Akiyama:2026dzg}, we apply this approach to the two-dimensional generalized $O(2)$ model and confirm that it successfully identifies the phase transitions between the ferromagnetic and nematic phases, as well as between the nematic and paramagnetic phases.

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Shinichiro Akiyama, Raghav G. Jha, Jun Maeda, Yuya Tanizaki, Judah Unmuth-Yockey. 2026-03-03. Tensor renormalization group approach to the $O(2)$ models via symmetry-twisted partition functions. https://arxiv.org/abs/2603.02739

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