Dynamical solutions of a quantum Heisenberg spin glass model

Abstract. We consider quantum-dynamical phenomena in the SU(2), S = 1/2 infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical selfconsistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complementary approximation schemes are applied: one restricts the quantum spin dynamics to a manageable number of Matsubara frequencies while the other employs an expansion in terms of the dynamical local spin susceptibility. We accurately determine the critical temperature Tc of the spin glass to paramagnet transition. We find that the dynamical correlations cause an increase of Tc by 2% compared to the result obtained in the spin-static approximation. The specific heat C(T ) exhibits a pronounced cusp at Tc. Contradictory to other reports we do not observe a maximum in the C(T )-curve above Tc.