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Solution of the Quantum Sherrington-Kirkpatrick Model

D. R. Grempel·M. J. Rozenberg
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Abstract

We solve the $S=1/2$ infinite-range random Heisenberg Hamiltonian in the paramagnetic phase using quantum Monte Carlo and analytical techniques. We find that the spin-glass susceptibility diverges at a finite temperature $T_g$ which demonstrates the existence of a low-temperature ordered phase. Quantum fluctuations reduce the critical temperature and the effective Curie constant with respect to their classical values. They also give rise to a redistribution of spectral weight in the dynamic structure factor in the paramagnetic phase. As the temperature decreases the spectrum of magnetic excitations gradually splits into quasi-elastic and inelastic contributions whose weights scale as $S^2$ and $S$ at low temperature.

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D. R. Grempel, M. J. Rozenberg. 1997-07-28. Solution of the Quantum Sherrington-Kirkpatrick Model. https://arxiv.org/abs/cond-mat/9707288

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