By solving the quench dynamics of a frustrated many-body spin-boson problem, we investigate the role of spin size on the dynamical formation of spin-glass order. In particular, we observe that quantum and classical spin glasses exhibit markedly different evolution. The former displays a quick relaxation of magnetization together with an exponential dependence of the spin-glass order parameter on spin size, while the latter has long-lasting prethermal magnetization and a spin-glass order parameter independent of spin size. The quantum-to-classical crossover is sharp and occurs for relatively small spins, highlighting the fragility of the quantum regime. Furthermore, we show that spin-glass order is resonantly enhanced when the frequency of the bosonic mediators of the interactions approaches the value of the transverse field. Our predictions are directly applicable to the nonequilibrium dynamics of all spin-glass systems with SU(2) spins, such as the quantum Sherrington-Kirkpatrick model, and they can be examined in recently developed multimode cavity QED experiments. Published by the American Physical Society 2024
By solving the quench dynamics of a frustrated many-body spin-boson problem, we investigate the role of spin size on the dynamical formation of spin-glass order. In particular, we observe that quantum and classical spin glasses exhibit markedly different evolution. The former displays a quick relaxation of magnetization together with an exponential dependence of the spin-glass order parameter on spin size, while the latter has long-lasting prethermal magnetization and a spin-glass order parameter independent of spin size. The quantum-to-classical crossover is sharp and occurs for relatively small spins, highlighting the fragility of the quantum regime. Furthermore, we show that spin-glass order is resonantly enhanced when the frequency of the bosonic mediators of the interactions approaches the value of the transverse field. Our predictions are directly applicable to the nonequilibrium dynamics of all spin-glass systems with SU(2) spins, such as the quantum Sherrington-Kirkpatrick model, and they can be examined in recently developed multimode cavity QED experiments. Published by the American Physical Society 2024
We consider the nonequilibrium behavior of the spin-glass ordered phase within the droplet scaling theory introduced previously. The fundamental long-time nonequilibrium process is assumed to be the thermally activated growth of spin-glass ordered domains. The remanent magnetization, m(t), in zero field is found to decay at long times as m(t)\ensuremath{\sim}${R}_{t}^{\mathrm{\ensuremath{-}}\ensuremath{\lambda}}$, where Rt\ensuremath{\sim}(lnt${)}^{1/\ensuremath{\psi}}$ is the linear domain size, \ensuremath{\psi} is the previously introduced barrier exponent describing the growth of activation-barrier heights with length scale, and \ensuremath{\lambda} is a new nonequilibrium dynamic exponent, satisfying the relation \ensuremath{\lambda}\ensuremath{\ge}d/2 for d-dimensional systems. The effects of waiting for partial equilibration before making a measurement are studied in various regimes. The effects of quenching first to one temperature and then to another are also examined. Such experiments can, in principle, be used to obtain information about the relative rate of dynamic evolution as well as the overlap between the equilibrium states at different temperatures. In particular, the length scale ${L}_{\ensuremath{\Delta}T}$, below which equilibrium correlations at temperatures T and T+\ensuremath{\Delta}T are similar, plays an important role. The decay of m(t) and the growth of spin-glass order after a quench are examined in Monte Carlo simulations of the Sherrington-Kirkpatrick model.
We realize a driven-dissipative Ising spin glass using cavity QED in a novel "4/7" multimode geometry. Gases of ultracold atoms trapped within the cavity by optical tweezers serve as effective spins. They are coupled via randomly signed, all-to-all Ising cavity-mediated interactions. Networks of up to n=25 spins are holographically imaged via cavity emission. The system is driven through a frustrated transverse-field Ising transition, and we show that the entropy of the spin glass states depends on the rate at which the transition is crossed. Despite being intrinsically nonequilibrium, the system exhibits phenomena associated with Parisi's theory of equilibrium spin glasses, namely, replica symmetry breaking (RSB) and ultrametric structure. For system sizes up to n=16, we measure the Parisi function q(x), Edwards-Anderson overlap q_{EA}, and ultrametricity K correlator; all indicate a deeply ordered spin glass under RSB. The system can serve as an associative memory and enable aging and rejuvenation studies in driven-dissipative spin glasses at the microscopic level.
Light-matter interfaces have now entered a new stage marked by the ability to engineer quantum correlated states under driven-dissipative conditions. To propel this new generation of experiments, we are confronted with the need to model nonunitary many-body dynamics in strongly coupled regimes by transcending traditional approaches in quantum optics. In this work, we contribute to this program by adapting a functional-integral technique, conventionally employed in high-energy physics, in order to obtain nonequilibrium dynamics for interacting light-matter systems. Our approach is grounded in constructing “two-particle irreducible” (2PI) effective actions, which provide a nonperturbative and conserving framework for describing quantum evolution at a polynomial cost in time. We apply our method to complement the analysis of spin-glass formation in the context of frustrated multimode cavity quantum electrodynamics, initiated in our accompanying work [Hosseinabadi , ]. Finally, we outline the capability of the technique to describe other near-term platforms in many-body quantum optics, and its potential to make predictions for this new class of experiments. Published by the American Physical Society 2024
Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here, we study quantum dynamics of an isolated 1D spin glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via a resonance avalanche mechanism, that is also responsible for the destruction of MBL in nonglassy systems with power-law interactions. At low energy densities, the interaction-induced fields obtain a power-law soft gap, making the resonance avalanche mechanism inefficient. This leads to the persistence of the spin-glass order, as demonstrated by resonance analysis and by numerical studies. A small fraction of resonant spins forms a thermalizing system with long-range entanglement, making this regime distinct from the conventional MBL. The model considered can be realized in systems of trapped ions, opening the door to investigating slow quantum dynamics induced by glassiness.
We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass.A close connection between open quantum dynamics and replica symmetry breaking is established, in which individual quantum trajectories are the replicas.We observe that entanglement plays an important role in the emergence of replica symmetry breaking in a fully connected, frustrated spin network of up to 15 spin-1=2 particles.Quantum trajectories of entangled spins reach steady-state spin configurations of lower energy than that of semiclassical trajectories.Cavity emission allows monitoring of the continuous stochastic evolution of spin configurations, while backaction from this projects entangled states into states of broken Ising and replica symmetry.The emergence of spin glass order manifests itself through the simultaneous absence of magnetization and the presence of nontrivial spin overlap density distributions among replicas.Moreover, these overlaps reveal incipient ultrametric order, in line with the Parisi replica symmetry breaking solution for the Sherrington-Kirkpatrick model.A nonthermal Parisi order parameter distribution, however, highlights the driven-dissipative nature of this quantum optical spin glass.This practicable system could serve as a test bed for exploring how quantum effects enrich the physics of spin glasses.
The crossover between quasiequilibrium and nonequilibrium spin-glass dynamics has been studied in Monte Carlo simulations of two- and three-dimensional short-range Ising spin-glass systems. The spin system was quenched in zero field to a low temperature T. After equilibrating for a time tw, a weak magnetic field was applied and the time dependence of the magnetization M(t) and the spin autocorrelation function q(t) was studied. Our results show that the relaxation rate S(t)=\ensuremath{\partial}M(t)/\ensuremath{\partial} log10(t) exhibits a maximum at t\ensuremath{\approxeq}tw. If the temperature is lowered or raised, immediately prior to the field application, the apparent age (ta) of the system, as defined by the maximum in relaxation rate, is shifted to longer or shorter time scales, respectively. No significant differences between the aging behavior in two and three dimensions are found. The relation \ensuremath{\chi}(t)=[1-q(t)]/T holds only for short time scales (t\ensuremath{\ll}tw), clear deviations are found at longer time scales (t>tw). Since this relation should according to the fluctuation-dissipation theorem hold for a system in equilibrium, this result is interpreted as an indication of a crossover between equilibrium and nonequilibrium dynamics. Our results are qualitatively in agreement with experiments as well as with theoretical models for the nonequilibrium spin-glass dynamics.