Multicriticality in "Even" and "Odd" Ising-Higgs Lattice Gauge Theories

The Ising–Higgs model is a paradigmatic example of phases and phase transitions that transcend the standard Landau–Ginzburg–Wilson framework. We investigate exotic critical phenomena along its self-dual line, focusing on two distinct regimes: the "even" vacuum sector and the "odd" finite-anyon-density sector. In the even sector, we employ a machine-learning technique based on real-space mutual information optimization to demonstrate that the Higgs–confinement multicritical point lacks a conserved current operator. This finding challenges conjectures proposing an emergent U(1) symmetry at the intersection of Ising* critical lines. In the odd sector, the Higgs and confinement transitions become fundamentally intertwined with valence-bond-solid (VBS) order due to geometric frustration, leading to an intersection of U(1)* critical lines. Our DMRG simulations reveal a simultaneous transition involving Higgs–confinement physics, self-duality breaking, and VBS ordering. Notably, the VBS order exhibits a cascade of incommensurate patterns with progressively increasing length scales before ultimately giving way to a quantum paramagnet. If time permits, I will also discuss a novel statistical-mechanics representation of the Ising–Higgs model that maps the Monte Carlo sampling problem onto a linear-algebra problem and greatly alleviates critical slowing down.