Quantum Loops, an Infinite Hierarchy of Multicritical Points in 2+1D.

Quantum loop emergent from spin system realizes strongly interacting states. We report a series of critical systems where fluctuation of deconfined large loops give qualitatively new phenomena -- topologically constrained dynamics of loops determines low-energy excitation; topologically different ways to reconnect loops dictates operator contents. Interestingly, these states also exhibit a rich structure of unusual ground state degeneracy below the continuous gapless spectrum, generalizing the topological degeneracy in gapped systems and Anderson tower in gapless systems. In particular, we report a special case realizing multicritical point between Z2-trivial and Z2-SPT phases in 2+1D.