Dynamical solutions of a quantum Heisenberg spin glass model

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 self-consistency 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 T <Subscript> c </Subscript> of the spin glass to paramagnet transition. We find that the dynamical correlations cause an increase of T <Subscript> c </Subscript> by <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$2\%$</EquationSource> </InlineEquation> compared to the result obtained in the spin-static approximation. The specific heat C(T) exhibits a pronounced cusp at T <Subscript> c </Subscript>. Contradictory to other reports we do not observe a maximum in the C(T)-curve above T <Subscript> c </Subscript>. Copyright Springer-Verlag Berlin/Heidelberg 2004