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Physics of the Solid State

Nonequilibrium dynamics of quantum spin glass in an AC magnetic field

Gaetano Busiello, R. V. Saburova, V. G. Sushkova, G. P. Chugunova

Published Feb 1, 2004• 4 citations
Publisher

Abstract

The ageing effect is studied analytically in a disordered quantum system interacting with its surroundings and subjected to an external ac magnetic field. Energy dissipation is due to the interaction of the system with a set of independent harmonic oscillators, imitating a quantum thermal bath. Dynamic equations for the autocorrelation function and linear-response function are derived using the method of closed-path integrals. The effect of an external field is studied on the correlation function and response in the spin-glass and paramagnetic phases. Both functions are found to depend on the spin interaction strength.

DOI
10.1134/1.1649431

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The ageing effect is studied analytically in a disordered quantum system interacting with its surroundings and subjected to an external ac magnetic field. Energy dissipation is due to the interaction of the system with a set of independent harmonic oscillators, imitating a quantum thermal bath. Dynamic equations for the autocorrelation function and linear-response function are derived using the method of closed-path integrals. The effect of an external field is studied on the correlation function and response in the spin-glass and paramagnetic phases. Both functions are found to depend on the spin interaction strength.
This work is devoted to a theoretical study of effects of aging in a disordered quantum system being in contact with an interior surroundings and subject to the influence of external alternating fields. The dissipation is realized via coupling with a set of independent harmonic oscillators, which imitate a quantum thermostat (bath), and with an external field. Using the formalism of closed-path integrals, dynamic equations are derived for the autocorrelation and linear-response functions. The dependences of correlation, response, and integrated-response functions on temperature, waiting time, and quantum parameter are studied. The effect of external fields on the behavior of these functions is analyzed. A qualitative agreement with experimental data have been found.
We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the p spin glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely, aging, survives the quantum fluctuations. In the subcritical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin glasses and the relevance of the effective temperatures with respect to the understanding of the low-temperature dynamics.
We study the long time dynamics of quantum spin glasses of rotors using the nonequilibrium Schwinger-Keldysh formalism. These models are known to have a quantum phase transition from a paramagnetic to a spin-glass phase, which we approach by looking at the divergence of the spin-relaxation rate at the transition point. In the aging regime, we determine the dynamical equations governing the time evolution of the spin response and correlation functions, and show that all terms in the equations that arise solely from quantum effects are irrelevant at long times under time reparametrization group (RPG) transformations. At long times, quantum effects enter only through the renormalization of the parameters in the dynamical equations for the classical counterpart of the rotor model. Consequently, quantum effects only modify the out-of-equilibrium fluctuation-dissipation relation (OEFDR), i.e. the ratio X between the temperature and the effective temperature, but not the form of the classical OEFDR.
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.