An Atlas of Classical Pyrochlore Spin Liquids (2411.03547v2)

Abstract: Frustrated magnetism in the pyrochlore lattice magnet has proven to be a most fruitful setting for the experimental and theoretical search for spin liquids. Besides the canonical case of spin ice, recent works have identified a variety of new classical and quantum spin liquids engendered by the generic nearest-neighbor anisotropic spin Hamiltonian for that lattice. However, a general framework for the thorough and systematic classification and characterization of these exotic states of matter has been lacking, as has an exhaustive list of all possible spin liquids that this model can support and, perhaps most interesting, what is the corresponding structure of their emergent field theory description. In this work, we develop such a theoretical framework to identify the interaction parameters stabilizing different classical spin liquids and derive their corresponding effective generalized Gauss's laws at low temperatures. Combining this with Monte Carlo simulations, we systematically identify all classical spin liquids for the general nearest-neighbor anisotropic spin Hamiltonian on the pyrochlore lattice. In doing so, we uncover new spin liquid models with exotic forms of generalized Gauss's law and multipole conservation laws. Our approach allows us to compile an atlas of all spin liquids realized in the phase diagram, providing a global picture of their mutual connections in parameter space and transitions between them. Our work will inform future theoretical and experimental studies of classical and quantum spin liquids on the pyrochlore lattice and help rationalize the exotic properties of pyrochlore magnets.