Classical theory shows that large communities are destabilized by random interactions among species pairs, creating an upper bound on ecosystem diversity. However, species interactions often occur in high-order combinations, whereby the interaction between two species is modulated by one or more other species. Here, by simulating the dynamics of communities with random interactions, we find that the classical relationship between diversity and stability is inverted for high-order interactions. More specifically, while a community becomes more sensitive to pairwise interactions as its number of species increases, its sensitivity to three-way interactions remains unchanged, and its sensitivity to four-way interactions actually decreases. Therefore, while pairwise interactions lead to sensitivity to the addition of species, four-way interactions lead to sensitivity to species removal, and their combination creates both a lower and an upper bound on the number of species. These findings highlight the importance of high-order species interactions in determining the diversity of natural ecosystems.
Recovering an unknown Hamiltonian from measurements is an increasingly important task for certification of noisy quantum devices and simulators. Recent works have succeeded in recovering the Hamiltonian of an isolated quantum system with local interactions from long-ranged correlators of a single eigenstate. Here, we show that such Hamiltonians can be recovered from local observables alone, using computational and measurement resources scaling linearly with the system size. In fact, to recover the Hamiltonian acting on each finite spatial domain, only observables within that domain are required. The observables can be measured in a Gibbs state as well as a single eigenstate; furthermore, they can be measured in a state evolved by the Hamiltonian for a long time, allowing to recover a large family of time-dependent Hamiltonians. We derive an estimate for the statistical recovery error due to approximation of expectation values using a finite number of samples, which agrees well with numerical simulations.
We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two distinct models of one-dimensional disordered and interacting spin chains. The obtained phase diagram for a well-studied model of the many-body localization transition shows excellent agreement with previously known results obtained from time-independent entanglement spectra. For a periodically driven model featuring an inherently dynamical time-crystalline phase, the phase diagram that our network traces coincides with an order parameter for its expected phases.
Subjecting a many-body localized system to a time-periodic drive generically leads to delocalization and a transition to ergodic behavior if the drive is sufficiently strong or of sufficiently low frequency. Here we show that a specific drive can have an opposite effect, taking a static delocalized system into the many-body localized phase. We demonstrate this effect using a one-dimensional system of interacting hard-core bosons subject to an oscillating linear potential. The system is weakly disordered, and is ergodic absent the driving. The time-periodic linear potential leads to a suppression of the effective static hopping amplitude, increasing the relative strengths of disorder and interactions. Using numerical simulations, we find a transition into the many-body localized phase above a critical driving frequency and in a range of driving amplitudes. Our findings highlight the potential of driving schemes exploiting the coherent destruction of tunneling for engineering long-lived Floquet phases. DOI: 10.1103/PhysRevB.96.020201Introduction. A key obstacle in the search for new nonequilibrium quantum phases of matter is the tendency of closed quantum many-body systems to indefinitely absorb energy from a time-periodic driving field. Thus, in the long time limit, such systems generically reach a featureless infinite-temperature-like state with no memory of their initial conditions [1][2][3][4][5][6][7][8]. Interestingly, this infinite temperature fate can be avoided by the addition of disorder [9][10][11][12][13]. Sufficiently strong disorder added to a clean interacting system may lead to a many-body localized (MBL) phase [14-18] which does not allow transport of energy and particles. The MBL phase can persist in the presence of a weak, high-frequency drive [9][10][11][12][13]. Periodically driven systems in the MBL phase retain memory of their initial conditions for arbitrarily long times. Thus, they can support nonequilibrium quantum phases of matter, including some which are unique to the nonequilibrium setting [19][20][21][22][23][24][25][26][27][28][29][30].Generically, subjecting an MBL system to a periodic drive increases the localization length [9][10][11]. If the driving is done at sufficiently low frequencies or high amplitudes, it may even cause the system to exit the MBL phase. This delocalization effect is caused by transitions such as photon-assisted hopping, which are mediated by the periodic drive. These transitions conserve energy only modulohω, and can therefore lead to new many-body resonances which destabilize localization.An oscillating linear potential (henceforth an ac electric field) has a more subtle effect, as it can effectively suppress the hopping amplitude between adjacent lattice sites. This effect, called dynamical localization [34] or coherent destruction of tunneling [35], has been implemented in cold atoms [36][37][38], and can be used, for example, to induce a transition from a superfluid to a Mott insulator [39,40]. In noninteracting systems, dynamical localization can be e...
Recent works have shown that generic local Hamiltonians can be efficiently inferred from local measurements performed on their eigenstates or thermal states. Realistic quantum systems are often affected by dissipation and decoherence due to coupling to an external environment. This raises the question whether the steady states of such open quantum systems contain sufficient information allowing for full and efficient reconstruction of the system's dynamics. We find that such a reconstruction is possible for generic local Markovian dynamics. We propose a recovery method that uses only local measurements; for systems with finite-range interactions, the method recovers the Lindbladian acting on each spatial domain using only observables within that domain. We numerically study the accuracy of the reconstruction as a function of the number of measurements, type of opensystem dynamics and system size. Interestingly, we show that couplings to external environments can in fact facilitate the reconstruction of Hamiltonians composed of commuting terms.
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