General Quantum Spin Liquids

We investigate the effects of frustration in magnetic systems on the pyrochlore lattice, looking at both conventional frustrated magnetism as well as a less-studied form of frustration known as kinetic frustration. Starting at half-filling, we study the stability of the classical Heisenberg spin liquid phase upon including further-neighbour interactions. Our findings indicate that any second and/or third nearest-neighbor interactions lead to ordering. Specifically, we characterise a new kind of ordered state, where pairs of sublattices form antiparallel spirals. As an alternative route to frustrate the pyrochlore magnet, we then proceed to dope an S= 1/2 system deep in the Mott regime. We find that this kinetic frustration has the potential to induce a spin liquid, and more particularly, the long sought-after resonating valence bond spin liquid originally proposed by Anderson. We prove that the resonating valence bond spin liquid is the ground state of the infinite-U Hubbard model in the thermodynamic limit. Numerical computations further show that this result also holds for finite systems and upon adding small antiferromagnetic and ferromagnetic Heisenberg exchange. While much attention has been devoted to the emergence of new states from geometrically frustrated exchange, our work demonstrates that kinetic energy frustration in doped Mott insulators may be pivotal to stabilising robust quantum spin liquids in real materials.