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

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.

7+6 pages, 8+1 figures

References in corpus (5)

• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• Different faces of confinement
• Percolation as a confinement order parameter in ${\mathbb{Z}}_2$ lattice gauge theories

Cited by in corpus (3)

• Independent e- and m-anyon confinement in the parallel field toric code on non-square lattices
• ParaToric 1.0: Continuous-time quantum Monte Carlo for the toric code in a parallel field
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions