We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.

We use extensive numerical simulations based on matrix product state methods to study the quantum dynamics of spin chains with strong on-site disorder and power-law decaying (1/r α ) interactions. We focus on two spin-1/2 Hamiltonians featuring power-law interactions: Heisenberg and XY and characterize their corresponding long-time dynamics using three distinct diagnostics: decay of a staggered magnetization pattern I(t), growth of entanglement entropy S(t), and growth of quantum Fisher information FQ(t). For sufficiently rapidly decaying interactions α > αc we find a many-body localized phase, in which I(t) saturates to a non-zero value, entanglement entropy grows as S(t) ∝ t 1/α , and Fisher information grows logarithmically. Importantly, entanglement entropy and Fisher information do not scale the same way (unlike short range interacting models). The critical power αc is smaller for the XY model than for the Heisenberg model.

High precision macroscopic quantum control in interacting light-matter systems remains a significant goal toward novel information processing and ultra-precise metrology. We show that the out-of-equilibrium behavior of a paradigmatic light-matter system (Dicke model) reveals two successive stages of enhanced quantum correlations beyond the traditional schemes of near-adiabatic and sudden quenches. The first stage features magnification of matter-only and light-only entanglement and squeezing due to effective nonlinear self-interactions. The second stage results from a highly entangled light-matter state, with enhanced superradiance and signatures of chaotic and highly quantum states. We show that these new effects scale up consistently with matter system size, and are reliable even in dissipative environments.Many-body quantum dynamics are at the core of many natural and technological phenomena, from understanding of superconductivity or magnetism, to applications in quantum information processing as in adiabatic quantum computing [1]. Critical phenomena, defect formation, symmetry breaking, finite-size scaling are all aspects that emerge from the collective properties of the system [2]. Spin networks, many-body systems composed of the simplest quantum unit, are an obvious starting point to understand those phenomena, as they enclose much of their complex behavior in a highly controllable and tractable way. However, if the system under investigation includes a radiation subsystem, new opportunities arise for monitoring and characterizing the resulting collective phenomena [3,4]. By devising driving protocols of the light-matter interaction, high precision macroscopic control then becomes a possibility, regardless of whether the focus is on the matter subsystem, the light, or the composite manipulation of both. This is particularly true for the Dicke model (DM) [5], which is the subject of the present work.The DM describes a radiation-matter system which, despite its simplicity, exhibits a wide arrange of complex collective phenomena, many of them specifically associated with the existence of a quantum phase transition (QPT) [6]. Experimental realizations of the DM have been presented in different settings, from proposed realizations in circuit quantum electrodynamics [7], to the recent very successful demonstrations of DM superradiance in various cold atom experiments [8]. While the light and matter properties in the equilibrium ground state are relatively well known [9][10][11][12][13], its fully quantum out-of-equilibrium critical behavior is just starting to be understood [14,15].In the DM, both the matter and field are known to act as mediators of an effective nonlinear self-interaction involving each other [10,13]. These nonlinear interactions produce interesting phenomena in both atomic and optical systems [16,17]. Among the most relevant effects, there is the strong collapse and revival of squeezing [18,19], which in many matter states can be related to atom-atom entanglement [20]. Applications of such eff...

The Discrete Truncated Wigner Approximation (DTWA) is a semi-classical phase space method useful for the exploration of Many-body quantum dynamics. In this work we investigate ManyBody Localization (MBL) and thermalization using DTWA and compare its performance to exact numerical solutions. By taking as a benchmark case a 1D random field Heisenberg spin chain with short range interactions, and by comparing to numerically exact techniques, we show that DTWA is able to reproduce dynamical signatures that characterize both the thermal and the MBL phases. It exhibits the best quantitative agreement at short times deep in each of the phases and larger mismatches close to the phase transition. The DTWA captures the logarithmic growth of entanglement in the MBL phase, even though a pure classical mean-field analysis would lead to no dynamics at all. Our results suggest the DTWA can become a useful method to investigate MBL and thermalization in experimentally relevant settings intractable with exact numerical techniques, such as systems with long range interactions and/or systems in higher dimensions.