Infinite-range quantum random Heisenberg magnet

Abstract

We study with exact diagonalization techniques the Heisenberg model for a system of SU(2) spins with S = 1/2 and random infinite-range exchange interactions. We calculate the critical temperature Tg for the spin-glass to paramagnetic transition. We obtain Tg ≈ 0.13, in good agreement with previous quantum Monte Carlo and analytical estimates. We provide a detailed picture for the different kind of excitations which intervene in the dynamical response χ ′′ (ω, T ) at T = 0 and analyze their evolution as T increases. We also calculate the specific heat Cv(T ). We find that it displays a smooth maximum at TM ≈ 0.25, in good qualitative agreement with experiments. We argue that the fact that TM > Tg is due to a quantum disorder effect.

Dynamical Response of Quantum Spin-Glass Models atT=0

“…As an initial test for the consistency and accuracy of our method, the better-known RITF model was first considered and we computed the critical field for the paramagnetic spin-glass transition. We obtained G c ഠ 0.72J [19] which is in agreement with previously reported values [7][8][9]. As a second test, the GS energy was estimated with E GS ͑G 0, a 0͒ ഠ 20.180J which is also in good agreement with Parisi's two-step replica symmetry breaking result [12].…”

“…2 we show I͑v͒ for different system sizes and it is quite clear that the frequency v p for the onset of the plateau moves swiftly to lower frequencies. In fact, by performing a careful study of the scaling of v p with N for different values of G in the whole spin-glass phase, one always finds that it extrapolates fast to zero [19]. Moreover, it is also found that v p~e xp͓2a͑G͒N͔, where a͑G͒ is a positive defined decreasing function of G. The behavior of the order parameter q as a function of the transverse field is quite simple and, within our precision, it is consistent with q͑G͒ 1 4 ͑1 2 G͞G c ͒, therefore also qualitatively similar to the Landau theory results valid for the critical region [13,20].…”

Dynamical solutions of a quantum Heisenberg spin glass model

“…In the paramagnetic phase C(T ) monotonically increases as the temperature is lowered. Contrary to what was previously reported by other authors [8] in our results there is no indication of a broad maximum in the full dynamical C(T )-curve above T c . Merely the "conventional" spinstatic approximation which neglects the quantum dynamics altogether and omits all m = 0 terms in the internal energy formula (37) has such a feature ( fig.…”

“…S a,ν τ S b,µ τ ′ eff ≡ 0 for ν = µ. Our model differs slightly from the one with couplings of the type J ij i =j,ν S ν i S ν j that has been considered in other work [3,4,5,6,7,8]. In the paramagnetic phase, however, both model variants lead to identical effective actions and the results, particularly for the critical temperature, are thus directly comparable.…”

Weak-coupling study of decoherence of a qubit in disordered magnetic environments

“…In fact, for a 1D spin bath one expects to have stronger finite-size effects compared to the models to be studied in the rest of the paper: i.e., infinite-range models which are known to have much reduced finite-size effects. 22,28 Before leaving this numerical method section we would like to note that our method differs substantially from others that are based on the solution of finite-size clusters and cluster expansions. Those methods usually deal with a nondisordered model Hamiltonian, which is solved for a small system size.…”