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arXiv:1203.6585 · Physical Review Letters

Facilitated Spin Models of Dissipative Quantum Glasses

Beatriz Olmos, Igor Lesanovsky, Juan P. Garrahan

Published Jul 10, 2012• 68 citations
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Abstract

We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behavior. These models are the quantum analogs of the classical facilitated spin models. Just like their classical counterparts, quantum facilitated models display complex glassy dynamics despite the fact that their stationary state is essentially trivial. In these systems, dynamical arrest is a consequence of kinetic constraints and not of static ordering. These models display a quantum version of dynamic heterogeneity: the dynamics toward relaxation is spatially correlated despite the absence of static correlations. Associated dynamical fluctuation phenomena such as decoupling of time scales is also observed. Moreover, we find that close to the classical limit, quantum fluctuations can enhance glassiness, as recently reported for quantum liquids.

DOI
10.1103/physrevlett.109.020403

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We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behavior. These models are the quantum analogs of the classical facilitated spin models. Just like their classical counterparts, quantum facilitated models display complex glassy dynamics despite the fact that their stationary state is essentially trivial. In these systems, dynamical arrest is a consequence of kinetic constraints and not of static ordering. These models display a quantum version of dynamic heterogeneity: the dynamics toward relaxation is spatially correlated despite the absence of static correlations. Associated dynamical fluctuation phenomena such as decoupling of time scales is also observed. Moreover, we find that close to the classical limit, quantum fluctuations can enhance glassiness, as recently reported for quantum liquids.
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.
The glass phase and its quantum analog are prominent challenges of current non-equilibrium statistical mechanics and condensed matter physics. As a model system to study the transition from classical to quantum glassy dynamics, we propose a setup of laser driven three-level atoms trapped in an optical lattice. Tuning the strength of the laser driving to the intermediate level allows one to study the transition from a classical kinetically constrained model to the coherent regime. For strong driving, Rydberg excitations evolve analogously to defects in the one-spin facilitated model, a minimal model known to exhibit glassy dynamics. In our setup, the constraints result from the interplay between Rydberg interactions and the laser detuning from the Rydberg state. The emerging heterogeneous relaxation timescales are tuneable over several orders of magnitudes. In the opposite limit of weak driving of the intermediate level, we find an effective cluster model which describes the dynamics in a reduced subspace of the allowed number and positions of Rydberg excitations. This subspace is uniquely determined by the initial state and is characterized by a fixed number of clusters of Rydberg excitations. In addition, we investigate the influence of random fields on the classical relaxation. We find that the glassy dynamics can relax faster in the presence of weak random fields.
We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.
Quantum many-body systems with kinetic constraints exhibit intriguing relaxation dynamics. Recent experimental progress in the field of cold atomic gases offers a handle for probing the collective behavior of such systems, in particular, for understanding the interplay between constraints and disorder. Here, we explore a spin chain with facilitation constraints---a feature which is often used to model classical glass formers---together with disorder that originates from spin-spin interactions. The specific model we study, which is realized in a natural fashion in Rydberg quantum simulators, maps onto an XXXXXX chain with nonlocal disorder. Our study shows that the combination of constraints and seemingly unconventional disorder may lead to interesting nonequilibrium behavior in experimentally relevant setups.
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.
Long-range interacting models exhibit rich dynamical phenomena driven by deviations from collective descriptions. This work extends the study of these models to open quantum systems, focusing on the complex interplay between nonlocal interactions and local dissipation. The results demonstrate that the impact of long-range interactions on relaxation is twofold: they mitigate the impact of noises by stabilizing ferromagnetic domains and reducing local fluctuation, yet simultaneously accelerate memory loss by indirectly exposing each spin to a broader environment. While strong dissipation drives the system into glassy, range-insensitive relaxation, the results in weak dissipation regime reveal rich state-dependent dynamics. Specifically, long-range collective behaviors protect the early-stage coherence of systems quenched from polarized states, whereas they actively accelerate the relaxation of staggered configurations. Furthermore, nonlocal interactions continue to drive memory decorrelation even in the near-steady stages of a dissipative quench. These findings offer timely theoretical insights for the design, control, and calibration of analog quantum simulators operating with long-range interactions.