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Register a new userEquivalent dynamical complexity in a many-body quantum and collective human system
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Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding of Fratini et al. concerning quantum many-body effects in cuprate superconductors (i.e. scale of 10^{-9} - 10^{-4} meters and 10^{-12} - 10^{-6} seconds), (ii) explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism (i.e. scale of 10^3 - 10^6 meters and 10^4 - 10^8 seconds), (iii) shows consistency with various established empirical facts for financial markets, neurons and human gangs and (iv) makes microscopic sense for each application. Our findings also suggest that a potentially productive shift can be made in Complexity research toward the identification of equivalent many-body dynamics in both classical and quantum regimes.
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Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics.
Dynamical quantum phase transitions (DQPTs) extend the concept of phase transitions and thus universality to the non-equilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transverse-field Ising models. We observe non-equilibrium dynamics induced by a quantum quench and show for strings of up to 10 ions the direct detection of DQPTs by measuring a quantity that becomes non-analytic in time in the thermodynamic limit. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
We demonstrate that arbitrary time evolutions of many-body quantum systems can be reversed even in cases when only part of the Hamiltonian can be controlled. The reversed dynamics obtained via optimal control --contrary to standard time-reversal procedures-- is extremely robust to external sources of noise. We provide a lower bound on the control complexity of a many-body quantum dynamics in terms of the dimension of the manifold supporting it, elucidating the role played by integrability in this context.
In this letter, we study the PXP Hamiltonian with an external magnetic field that exhibits both quantum scar states and quantum criticality. It is known that this model hosts a series of quantum many-body scar states violating quantum thermalization at zero magnetic field, and it also exhibits an Ising quantum phase transition driven by finite magnetic field. Although the former involves the properties of generic excited states and the latter concerns the low-energy physics, we discover two surprising connections between them, inspired by the observation that both states possess log-volume law entanglement entropies. First, we show that the quantum many-body scar states can be tracked to a set of quantum critical states, whose nature can be understood as pair-wisely occupied Fermi sea states. Second, we show that the partial violation of quantum thermalization diminishes in the quantum critical regime. We envision that these connections can be extended to general situations and readily verified in existing cold atom experimental platforms.
The collective and quantum behavior of many-body systems may be harnessed to achieve fast charging of energy storage devices, which have been recently dubbed quantum batteries. In this paper, we present an extensive numerical analysis of energy flow in a quantum battery described by a disordered quantum Ising chain Hamiltonian, whose equilibrium phase diagram presents many-body localized (MBL), Anderson localized (AL), and ergodic phases. We demonstrate that i) the low amount of entanglement of the MBL phase guarantees much better work extraction capabilities than the ergodic phase and ii) interactions suppress temporal energy fluctuations in comparison with those of the non-interacting AL phase. Finally, we show that the statistical distribution of values of the optimal charging time is a clear-cut diagnostic tool of the MBL phase.
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