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

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Main Authors: Dünnweber, Gesa, Linsel, Simon M., Bohrdt, Annabelle, Grusdt, Fabian
Format: Preprint
Published: 2024
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_version_ 1866916607370985472
author Dünnweber, Gesa
Linsel, Simon M.
Bohrdt, Annabelle
Grusdt, Fabian
author_facet Dünnweber, Gesa
Linsel, Simon M.
Bohrdt, Annabelle
Grusdt, Fabian
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_17515
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Percolation renormalization group analysis of confinement in $\mathbb{Z}_2$ lattice gauge theories
Dünnweber, Gesa
Linsel, Simon M.
Bohrdt, Annabelle
Grusdt, Fabian
Statistical Mechanics
Strongly Correlated Electrons
High Energy Physics - Lattice
Quantum Physics
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.
title Percolation renormalization group analysis of confinement in $\mathbb{Z}_2$ lattice gauge theories
topic Statistical Mechanics
Strongly Correlated Electrons
High Energy Physics - Lattice
Quantum Physics
url https://arxiv.org/abs/2406.17515