Disordered Quantum-entangled Symmetry-enriched U (1) exotic 3D Quantum Spin Liquid (QSL) Phase in Dipolar-Octupolar pseudospin, effective spin-(1/2) Pyrochlores Magnets Ce₂X₂O₇, (X=Zr, Hf).

Search for novel symmetry enriched QSLs topological magnets with fractionalized excitations become important. Pauling’s Ice-rule model of frustration, lead to ground state residual finite entropy, redeemed in pyrochlore hosting a classical Coulomb phase in Spin-Ice (SI). QSI are promising proprietors for QSL. Ce₂X₂O₇ (X=Zr, Hf) are insulator with 4,5f¹ Ce³⁺ degrees of freedom decorating pyrochlore lattice, network of corner-sharing tetrahedra, archetype for 3D-geometrical frustration. Experiments on Ce₂X₂O₇ above T=0.05 K show no evidence of ordered state, suggests it may host novel QSI, 3D QSL with emergent photon. High energy neutron spectroscopy reveals crystal field ground state doublet originating from J=5/2, comprised m_J=±3/2, resulting pseudospin S_effective=1/2 degree of freedom, components transform as dipolar and octupolar moments under symmetry operations, arises from strong spin orbit coupling and crystal field effects. In octupole QSL, spin waves carry octupole moments, do not couple to neutron moments but contribute to field dependent heat capacity, hiding characteristic signatures from neutrons. In QSL collective spins excitations described by U (1) lattice gauge theory. Theoretical modelling of heat capacity, magnetic susceptibility and neutron scattering data estimates terms in near-neighbor microscopic effective XYZ Hamiltonian, supports presence of octupolar π-flux U (1) novel QSL, ordered All-In All-Out ground state near boundary of dipolar and octupolar nature.