Theoretical study of quantum spin liquids in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:math> hyper-hyperkagome magnets: Classification, heat capacity, and dynamical spin structure factor

Recent experiments suggest a quantum spin liquid ground state in the material PbCuTe$_2$O$_6$, where $S=1/2$ moments are coupled by antiferromagnetic Heisenberg interactions into three dimensional structure of corner sharing triangles dubbed hyper-hyperkagome lattice. It exhibits richer connectivity, and thus likely stronger geometric frustration, than relatively well studied hyperkagome Here, we investigate possible liquids magnet using complex fermion mean field theory. Extending results previous projective symmetry group analysis, identify only two $\mathbb{Z}_2$ $U(1)$ that compatible with structure. The has spinon Fermi surface. For liquids, one small excitation gap, while other is gapless proximate to liquid. We show gapped can principle be distinguished heat capacity measurements. Moreover, calculate dynamical factors all find they highly resemble inelastic neutron scattering spectra PbCuTe$_2$O$_6$. Implications our work experiments, as its relations existing theoretical studies, discussed.