Weak universality induced by $Q=\pm 2e$ charges at the deconfinement transition of a (2+1)-d $U(1)$ lattice gauge theory

TL;DR

This paper investigates how adding higher charged matter fields to a (2+1)-d U(1) lattice gauge theory induces a form of weak universality, where critical exponents vary continuously while their ratio remains fixed, extending classic universality concepts.

Contribution

It demonstrates for the first time that weak universality, with continuously varying critical exponents, occurs in lattice gauge theories when higher charged matter fields are introduced.

Findings

Finite temperature phase transition in the 2-d XY universality class.

Introduction of $Q= \pm 2e$ charges leads to weak universality.

Critical exponents $\gamma, u$ vary continuously with coupling.

Abstract

Matter-free lattice gauge theories (LGTs) provide an ideal setting to understand confinement to deconfinement transitions at finite temperatures, which is typically due to the spontaneous breakdown (at large temperatures) of the centre symmetry associated with the gauge group. Close to the transition, the relevant degrees of freedom (Polyakov loop) transform under these centre symmetries, and the effective theory only depends on the Polyakov loop and its fluctuations. As shown first by Svetitsky and Yaffe, and subsequently verified numerically, for the $U(1)$ LGT in $(2+1)$-d the transition is in the 2-d XY universality class, while for the $Z_2$ LGT, it is in the 2-d Ising universality class. We extend this classic scenario by adding higher charged matter fields, and show that the notion of universality is generalized such that the critical exponents $\gamma, \nu$ can change continuously as a coupling is varied, while their ratio is fixed to the 2-d Ising value. While such weak universality is well-known for spin models, we demonstrate this for LGTs for the first time. Using an efficient cluster algorithm, we show that the finite temperature phase transition of the $U(1)$ quantum link LGT in the spin $S=\frac{1}{2}$ representation is in the 2-d XY universality class, as expected. On the addition of $Q = \pm 2e$ charges distributed thermally, we demonstrate the occurrence of weak universality.