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In the literature, spin liquids are only possible in Mott insulators, however, I'm not entirely sure why the nuclear spin can't create a spin liquid in a band insulator.

Is this possible? If so, is there any specific reasons that it is not mentioned in the literature? If it is not possible, why not?

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There are few relevant points: the first is that we very rarely consider the magnetism of nuclear moments in a solid because the nuclear magneton is about 2000 times smaller than the Bohr magneton. So we're really stuck with electrons as the only relevant degrees of freedom for magnetism.

But, let's imagine for a minute that we could kick out the electrons. The whole point of a spin liquid is to be driven to paramagnetism at low temperatures by quantum fluctuations. The high ordering temperature scales in typical magnets are set by the "exchange" scale (of electrons literally, though virtually, exchanging places in the solid). Dipole-dipole interactions are not strong enough to be the origin of magnetism in solids (this was a big deal in the early days of quantum mechanics!) and dipolar interactions between nuclear spins even more so; so functionally, it would be impossible to determine experimentally if such a system was a spin liquid or just a thermally disordered paramagnet even at the lowest possible experimental temperatures.

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