Percolation renormalization group analysis of confinement in $\mathbb{Z}_2$ lattice gauge theories
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |