Spin freezing and the Sachdev-Ye model (Vol. 50, No. 2)

Generic phase diagram of unconventional superconductors showing a bad metal phase with frozen magnetic moments crossing over into Fermi liquid metal. The crossover regime with fluctuating moments is effectively described by the Sachdev-Ye model.

The infinite-range, random-exchange Heisenberg spin model introduced in 1993 by Sachdev and Ye describes a non-Fermi liquid metal without quasi-particles, which resembles the bad-metal state of unconventional superconductors. Because of the somewhat artificial nature of the model, it is however not obvious how to connect this result to phenomena observed in strongly correlated materials. The latter are typically described by the Hubbard model and its multi-orbital extensions. Interestingly, the same non-Fermi liquid exponents as in the Sachdev-Ye model are generically observed in the correlated metallic phase of multi-orbital Hubbard models with Hund coupling. Our analysis suggests that the Sachdev-Ye model can be regarded as an effective description of a spin-freezing crossover regime with fluctuating local moments and that the variance of the random coupling in the Sachdev-Ye model is related to the Hund coupling. This analogy provides new insights into the nature of non-Fermi liquid metals, and into the close connection between spin freezing and unconventional superconductivity.

Ph. Werner, A.J. Kim and Sh. Hoshino, Spin freezing and the Sachdev-Ye model, EPL 124, 57002 (2018)