Atlas of pyrochlore CSLs in the large-N limit

The pyrochlore lattice spin system has been one of the most fruitful platforms in the search for spin liquids, both experimentally and theoretically. In this work, we develop the field theory for the emergence of generalized Gauss’s law constraints on the pyrochlore lattice and use it to systematically construct various (if not all) spin liquids in the large-N limit with nearest neighbor interactions. We also perform Monte Carlo simulations to examine what happens to these models with classical vector spins.



These results provide us with an atlas of spin liquid regimes on the phase diagram of the pyrochlore spin model. We find new spin liquid models with exotic forms of generalized Gauss’s law and multipole conservations and develop a better understanding of how different classical spin liquids transition into each other. Our work also serves as a treasure map for potential quantum spin liquids in quantum pyrochlore systems.