Phenomenological Theory of Coulombic Quantum Spin Liquids

Coulombic quantum spin liquids (C-QSLs) whose low energy excitations are U(1) gauge fluctuations realize massive quantum entanglement in quantum magnets. They have been suggested to be hosted in several three-dimensional materials including a pyrochlore structure, A2B2O7. In this study, we present a phenomenological theory of C-QSLs and their phase transitions in the extended Landau paradigm. Within extended Landau paradigm which can be achieved by enlarging symmetry group, we obtain richer phase diagrams than the conventional order only diagrams. As a specific example, we construct the effective theory of conventional order parameters of a lattice symmetry(G) and emergent excitations of C-QSLs(~G) in the extended Landau paradigm. Namely, we write down all terms respecting a lattice symmetry and gauge invariance and investigate possible phase structures. For example, we apply our theory to systems with an all-in-all-out (AIAO) order parameter and U(1) gauge fluctuation dubbed Coulombic AIAO (AIAO*). Phenomenologically we obtain characteristic heat capacities and magnetic responses characterizing phases. Our theory may be directly applied to an insulating pyrochlore system where both A and B sites are magnetically active and one of them forms a U(1) quantum spin liquids.