Heisenberg antiferromagnet on the pyrochlore lattice

We investigate the quantum Heisenberg model on the pyrochlore lattice for spin-1/2 in the presence of antiferromagnetic nearest-neighbor J₁, second nearest-neighbor J₂, and third nearest-neighbor J_3a exchange interactions. By employing the pseudofermion functional renormalization group method, we find, that the quantum Coulomb spin liquid of the J₁ only model is robust along the line J=J₂=J_3a up till J/J₁∼0.22, thus extending its classical region of stability. Similarly, for J/J₁>0.22, we find an absence of long-range magnetic order down to T=J₁/100, however, the bowtie features now give way to half-moons as seen in the static spin susceptibility profile, thus pointing to the realization of a ``half-moon’’ quantum spin liquid. At the point J/J₁=1/2, which features a sub-extensively degenerate classical ground-state manifold, we show that quantum fluctuations fail to break this degeneracy stabilizing a quantum spin liquid. In stark contrast to this finding, in the corresponding classical model, thermal fluctuations are known to select a collinear antiferromagnetically ordered state via the order-by-disorder mechanism. Hence, we present a rare scenario wherein thermal and quantum fluctuations act differently.