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arXiv · 2406.17515

Percolation renormalization group analysis of confinement in $\mathbb{Z}_2$ lattice gauge theories

Gesa Dünnweber·Simon M. Linsel·Annabelle Bohrdt·Fabian Grusdt
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Abstract

The analytical study of confinement in lattice gauge theories (LGTs) remains a difficult task to this day. Taking a geometric perspective on confinement, we develop a real-space renormalization group (RG) formalism for $\mathbb{Z}_2$ LGTs using percolation probability as a confinement order parameter. The RG flow we analyze is constituted by both the percolation probability and the coupling parameters. We consider a classical $\mathbb{Z}_2$ LGT in two dimensions, with matter and thermal fluctuations, and analytically derive the confinement phase diagram. We find good agreement with numerical and exact benchmark results and confirm that a finite matter density enforces confinement at $T<\infty$ in the model we consider. Our RG scheme enables future analytical studies of $\mathbb{Z}_2$ LGTs with matter and quantum fluctuations and beyond.

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Gesa Dünnweber, Simon M. Linsel, Annabelle Bohrdt, Fabian Grusdt. 2024-06-25. Percolation renormalization group analysis of confinement in $\mathbb{Z}_2$ lattice gauge theories. https://doi.org/10.1103/physrevb.111.024314

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