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arXiv:cond-mat/0412043 · International Journal of Modern Physics B

DISSIPATIVE QUANTUM DISORDERED MODELS

Leticia F. Cugliandolo

Published Jul 30, 2006• 2 citations
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Abstract

This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered – glassy – phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random king chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.

DOI
10.1142/s0217979206035308

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This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -- glassy -- phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random Ising chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.
This article reviews recent research on dissipative macroscopic quantum bosonic and fermionic systems. These studies address the following issues. (i) The existence of static and dynamic phase transitions; order of the critical lines and type of phases. (ii) The dynamics of systems that are unable to reach equilibrium with their (equilibrium) environment due to their intrinsic slow dynamics or driven by an external drive in the form of a time-dependent magnetic field, coupling to source and drain leads, etc. (iii) The development of an effective temperature that controls the large-scale dynamics and a two-time dependent decoherence phenomenon. (iv) The role played by the environment in the behaviour of the systems.
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 discuss the behavior of a quantum glassy system coupled to a bath of quantum oscillators. We show that the system localizes in the absence of interactions when coupled to a sub-Ohmic bath. When interactions are switched on localization disappears and the system undergoes a phase transition towards a glassy phase. We show that the position of the critical line separating the disordered and ordered phases strongly depends on the coupling to the bath. For a given type of bath, the ordered glassy phase is favored by a stronger coupling. Ohmic, sub-Ohmic, and super-Ohmic baths lead to different transition lines. We draw our conclusions from analysis of the partition function using the replicated imaginary-time formalism and from the study of the real-time dynamics of the coupled system using the Schwinger-Keldysh closed time-path formalism.
Zero-temperature or quantum phase transitions in itinerant electronic systems both with and without quenched disordered are discussed. Phase transitions considered include, the ferromagnetic transition, the antiferromagnetic transition, the superconductor-metal transition, and various metal-insulator transitions. Emphasis is placed on how to determine the universal properties that characterize these quantum phase transitions. For the first three of the phase transitions listed above, one of the main physical ideas established is that in zero-temperature systems there are soft or slow modes that exist in addition to the soft order parameter fluctuations, and that these modes can couple to the critical modes. These extra soft modes are shown to have a profound effect on the quantum critical properties. For quantum phase transitions involving zero wavenumber order parameters, i.e., the ferromagnetic and superconductor-metal transitions, these extra modes effectively lead to long-ranged effective interactions between order parameter fluctuations, which in turn lead to exactly soluble critical behaviors. For the antiferromagnetic case, we argue that while in low enough dimensions disorder fluctuation effects tend to destroy long-range order, quantum fluctuations counteract this effect and in some parameter regions manage to re-establish antiferromagnetic long-range order. For the metal-insulator transition, some recent new ideas are reviewed. In particular, it is pointed out that for interacting disordered electrons, one expects that in high dimensions the metal-insulator transition is related to the phase transition that occurs in random-field magnets in high dimensions. If the analogy also holds in three dimensions this suggests that the metal-insulator transition might have glassy characteristics.
We study the zero-temperature static properties of dissipative ensembles of quantum Ising spins arranged on periodic one-dimensional finite clusters and on an infinite chain. The spins interact ferro-magnetically with nearest-neighbor pure and random couplings. They are subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system using Monte Carlo simulations of the classical two-dimensional counterpart model. The coupling to the bath enhances the extent of the ordered phase, as found in mean-field spin glasses. In the case of finite clusters, we show that a generalization of the Caldeira-Leggett localization transition exists. In the case of the infinite random chain, we study the effect of dissipation on the transition and the Griffiths phase.