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Odd Toric Code in a tilted field: Higgs-confinement multicriticality, spontaneous self-duality symmetry breaking, and valence bond solids

2025/07/22 by Umberto Borla, Borla, Umberto, Ayush De +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Quantum, superfluid, helium dynamics #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2507.16523

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We investigate the quantum phase diagram of an ``odd'' variant of the two-dimensional Ising Fradkin--Shenker model, characterized by a uniform background of static e and m charges. Using large-scale tensor network and exact diagonalization methods, we determine the topology of the phase diagram, identifying an ``odd'' deconfined phase, confinement- and Higgs-induced valence bond solids (VBS), and a trivial paramagnet. Most notably, we uncover an exotic multicritical point along the self-dual line, where electric and magnetic excitations are related by an enriched ℤ2 duality. This transition is marked by the simultaneous onset of confinement, Higgs condensation, translational symmetry breaking, and spontaneous duality symmetry breaking. Within our numerical accuracy, the transition appears continuous, involving the softening of excitation gaps for e and m anyons at finite momentum. At intermediate couplings, we further identify VBS phases with enlarged unit cells, potentially indicating frustration-induced crystalline order beyond commensurate limits.

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