Simultaneous signatures of quantum spin liquid and broken symmetry in the Heisenberg spin-1/2 pyrochlore lattice

The antiferromagnetic spin-1/2 pyrochlore has been discussed as a quantum spin liquid (QSL) candidate. To study the ground state properties and identify phase transitions to adjacent ordered phases, we employ two variational approaches, many-variable Monte Carlo and Neural Quantum States. Validating our results against exact diagonalization on a 32-spin cluster, we expand to large-scale lattices up to 256 spins. We find that the magnetic correlations show pronounced features of the $k =0$ ordered phase upon inclusion of next-to-nearest-neighbor interactions and sharply vanish in the vicinity of the putative QSL, accompanied by an entanglement spectrum degeneracy and reduced susceptibility to twisted boundary conditions expected from a QSL. However, the QSL region is considerably smaller than expected from weak-coupling studies.
On the other hand, dimer correlations develop long-range order along with a vanishing symmetry gap, a signature of spontaneous inversion symmetry breaking. Finally, breaking the full $SU(2)$ symmetry down to a $U(1)$ model with Ising anisotropy leads to spin-nematic order. Our simultaneous observation of signatures associated with a QSL phase and long-range dimer and nematic correlations raises the prospect of the pyrochlore realizing broken-symmetry QSL.