Percolation as a confinement order parameter in $\mathbb{Z}_2$ lattice
gauge theories
- URL: http://arxiv.org/abs/2401.08770v2
- Date: Fri, 8 Mar 2024 13:15:13 GMT
- Title: Percolation as a confinement order parameter in $\mathbb{Z}_2$ lattice
gauge theories
- Authors: Simon M. Linsel and Annabelle Bohrdt and Lukas Homeier and Lode Pollet
and Fabian Grusdt
- Abstract summary: We propose percolation-inspired order parameters (POPs) to probe confinement of dynamical matter in $mathbbZ$ LGTs.
Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators.
- Score: 0.46873264197900916
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Lattice gauge theories (LGTs) were introduced in 1974 by Wilson to study
quark confinement. These models have been shown to exhibit (de-)confined
phases, yet it remains challenging to define experimentally accessible order
parameters. Here we propose percolation-inspired order parameters (POPs) to
probe confinement of dynamical matter in $\mathbb{Z}_2$ LGTs using electric
field basis snapshots accessible to quantum simulators. We apply the POPs to
study a classical $\mathbb{Z}_2$ LGT and find a confining phase up to
temperature $T=\infty$ in 2D (critical $T_c$, i.e. finite-$T$ phase transition,
in 3D) for any non-zero density of $\mathbb{Z}_2$ charges. Further, using
quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice
Fradkin-Shenker phase diagram at $T=0$ and explore the phase diagram at $T>0$.
The correlation length exponent coincides with the one of the 3D Ising
universality class and we determine the POP critical exponent characterizing
percolation. Our proposed POPs provide a geometric perspective of confinement
and are directly accessible to snapshots obtained in quantum simulators, making
them suitable as a probe for quantum spin liquids.
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