Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice

Using projective symmetry group analysis, we classify the possible quantum spin liquids on the S=1/2 breathing pyrochlore magnet, which results in 40 Z2 spin liquids and 16 U(1) spin liquids that respect the space group and the time reversal symmetry. As an application, we consider the antiferromagnetic Heisenberg model, which is proposed to be the dominant interaction in the candidate material Ba3Yb2Zn5O11. Focusing on the U(1) spin liquid Ansätze, we find that only two of them are physical when restricted to this model. We present an analytical solution to the parton mean field theory for each of these two U(1) spin liquids. It is revealed that one of them has gapless, while the other has gapped, spinon excitations, but they are equal in energy regardless of the degree of breathing anisotropy. The two U(1) spin liquids can be distinguished by the low temperature heat capacity contribution from the quadratically dispersing gapless spinons, which is further shown to be unaffected by gauge fluctuations within the random phase approximation. Finally, we demonstrate that a small Dzyaloshinskii-Moriya interaction lifts the degeneracy between the two U(1) spin liquids, and it eventually disconnects the lattice into independent tetrahedra at strong coupling. [Phys. Rev. B 106, 134402 (2022)]