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Building on quantum Monte Carlo simulations, we study the phase diagram of aone-parameter Hamiltonian interpolating between trivial and topological Isingparamagnets in two dimensions, which are dual to the toric code and the doublesemion. We discover an intermediate phase with stripe order which spontaneouslybreaks the protecting Ising symmetry. Remarkably, we find evidence that thisintervening phase is gapless due to the incommensurability of the stripepattern and that it is dual to a $U(1)$ gauge theory exhibiting Cantordeconfinement.

Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion