Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model

Abstract

We study the critical properties of the Ising-Higgs gauge theory in $(2+1)D$ along the self-dual line which have recently been a subject of debate. For the first time, using machine learning techniques, we determine the low energy operator content of the associated field theory. Our approach enables us to largely refute the existence of an emergent current operator and with it the standing conjecture that this transition is of the $X{Y}^{\ast }$ universality class. We contrast these results with the ones obtained for the $(2+1)D$ Ashkin-Teller transverse field Ising model where we find the expected current operator. Our numerical technique extends the recently proposed Real-Space Mutual Information allowing us to extract sub-leading non-linear operators. This allows a controlled and computationally scalable approach to target CFT spectrum and discern universality classes beyond $(1+1)D$ from Monte Carlo data.

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• Critical behavior of Fredenhagen-Marcu string order parameters at topological phase transitions with emergent higher-form symmetries
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Independent e- and m-anyon confinement in the parallel field toric code on non-square lattices
• Analytic framework for self-dual criticality in ${\mathbb{Z}}_k$ gauge theory with matter
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models
• O(5) multicriticality in the 3D two flavor SU(2) lattice gauge Higgs model