Translation-enriched Z2 and U(1) spin liquids with an application to alpha-RuCl3

The promising quasi-2d QSL candidate alpha-RuCl3 may realize a field-induced QSL with its nature yet known. We explore the possibility of a simplest gapped QSL description with emergent Z2 gauge fields (Z2 QSL), and study the spectroscopic and transport signals from emergent bosonic quasiparticles known as visons. We construct a model of Z2 QSL that aligns qualitatively with numerical results, and permutes topologically distinct visons upon one translation. The model fits the phenomenology of alpha-RuCl3, including low-field magnetic orders, spectroscopy and thermal hall signals at intermediate fields etc.

The results are built on a complete classification of translation-enriched Z2 orders. Translation actions in (3+1)d U(1) quantum spin liquids are also classified; in particular we show that the full duality of the free photon theory could be realized by translations.