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arXiv:cond-mat/0203537 · Physical review. B, Condensed matter

Infinite-range quantum random Heisenberg magnet

Liliana Arrachea, Marcelo J. Rozenberg

Published Jun 13, 2002• 29 citations
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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 ${T}_{g}$ for the spin-glass to paramagnetic transition. We obtain ${T}_{g}\ensuremath{\approx}0.13,$ 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 ${\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega},T)$ at $T=0$ and analyze their evolution as T increases. We also calculate the specific heat ${C}_{v}(T).$ We find that it displays a smooth maximum at ${T}_{M}\ensuremath{\approx}0.25,$ in good qualitative agreement with experiments. We argue that the fact that ${T}_{M}>{T}_{g}$ is due to a quantum disorder effect.

DOI
10.1103/physrevb.65.224430

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We study with exact diagonalization techniques the Heisenberg model for a system of SU(2) spins with S=1/2S=1/2S=1/2 and random infinite-range exchange interactions. We calculate the critical temperature Tg{T}_{g}Tg​ for the spin-glass to paramagnetic transition. We obtain Tg\ensuremath≈0.13,{T}_{g}\ensuremath{\approx}0.13,Tg​\ensuremath≈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 \ensuremathχ\ensuremath′′(\ensuremathω,T){\ensuremath{\chi}}^{\ensuremath{''}}(\ensuremath{\omega},T)\ensuremathχ\ensuremath′′(\ensuremathω,T) at T=0T=0T=0 and analyze their evolution as T increases. We also calculate the specific heat Cv(T).{C}_{v}(T).Cv​(T). We find that it displays a smooth maximum at TM\ensuremath≈0.25,{T}_{M}\ensuremath{\approx}0.25,TM​\ensuremath≈0.25, in good qualitative agreement with experiments. We argue that the fact that TM>Tg{T}_{M}>{T}_{g}TM​>Tg​ is due to a quantum disorder effect.
Using exact diagonalization techniques we study the dynamical response of the anisotropic disordered Heisenberg model for systems of S=1/2 spins with infinite range random exchange interactions at temperature T=0. The model can be considered as a generalization, to the quantum case, of the well known Sherrington-Kirkpatrick classical spin-glass model. We also compute and study the behavior of the Edwards Anderson order parameter and energy per spin as the anisotropy evolves from the Ising to the Heisenberg limits.
We solve the S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=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 Tg{T}_{g}Tg​ 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 quasielastic and inelastic contributions whose weights scale as S2{S}^{2}S2 and SSS at low temperature.
We solve the S=1/2S=1/2S=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 TgT_gTg​ 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 S2S^2S2 and SSS at low temperature.
We study the out-of-equilibrium dynamics of the infinite range quantum Heisenberg spin glass model coupled to a thermal relaxation bath. The SU(2)\mathrm{SU}(2)SU(2) spin algebra is generalized to SU(N)\mathrm{SU}(N)SU(N) and we analyze the large-NNN limit. The model displays a dynamical phase transition between a paramagnetic and a glassy phase. In the latter, the system remains out-of-equilibrium and displays an aging phenomenon, which we characterize using both analytical and numerical methods. In the aging regime, the quantum fluctuation-dissipation relation is violated and replaced over a very long time by its classical generalization, as in models involving simple spin algebras studied previously. We also discuss the effect of a finite coupling to the relaxation baths and their possible forms. This work completes and justifies previous studies on this model using a static approach.
We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field ΓΓΓ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of ΓΓΓ and for system sizes N≤16N \le 16N≤16. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of ΓΓΓ. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at Γc≃1.5Γ_c \simeq 1.5Γc​≃1.5. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get z=2.1±0.1z=2.1 \pm 0.1z=2.1±0.1 which is in contradiction with a recent estimate (z=4z=4z=4). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for Γ<ΓcΓ< Γ_cΓ<Γc​.