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Register a new userBose system critical dynamics near quantum phase transition
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We show that the change of the fluctuation spectrum near the quantum critical point (QCP) may result in the continuous change of critical exponents with temperature due to the increase in the effective dimensionality upon approach to QCP. The latter reflects the crossover from thermal fluctuations white noise mode to the quantum fluctuations regime. We investigate the critical dynamics of an exemplary system obeying the Bose-Einstein employing the Keldysh-Schwinger approach and develop the renormalization group technique that enables us to obtain analytical expressions for temperature dependencies of critical exponents.
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We study the dynamical response of a system to a sudden change of the tuning parameter $lambda$ starting (or ending) at the quantum critical point. In particular we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order $m$ at the quantum critical point, where $m$ is related to the power of the quench. Precisely for sudden quenches the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold atoms experiments.
A quasi one--dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particle density. Since it is a one dimensional transition, it takes place at zero temperature and therefore quantum fluctuations dominate. In [Fishman, et al., Phys. Rev. B 77, 064111 (2008)] it was shown that the system close to the linear-zigzag instability is described by a $phi^4$ model. We propose a mapping of the $phi^4$ field theory to the well known Ising chain in a transverse field, which exhibits a quantum critical point. Based on this mapping, we estimate the quantum critical point in terms of the system parameters. This estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs, and which has a finite, measurable deviation from the critical point evaluated within the classical theory. A measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures T. We focus in particular on a trapped ion system, and estimate the implied limitations on T and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is in principle accessible.
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the theory of HPT, it is still incomplete, particularly when the transition is induced by cluster merging dynamics. Here, we aim to develop a theoretical framework of the HPT induced by such dynamics. We find that two correlation-length exponents are necessary for characterizing the giant cluster and finite clusters, respectively. Finite-size scaling method for the HPT is also introduced. The conventional formula of the fractal dimension in terms of the critical exponents is not valid. Neither the giant nor finite clusters are fractals but they have fractal boundaries.
The characterization of entanglement is a central problem for the study of quantum many-body dynamics. Here, we propose the quantum Fisher information as a useful tool for the study of multipartite-entanglement dynamics in many-body systems. We illustrate this by considering the regular-to-ergodic transition in the Dicke model---a fully-connected spin model showing quantum thermalization above a critical interaction strength. We show that the QFI has a rich dynamical behavior which drastically changes across the transition. In particular, the asymptotic value of the QFI, as well as its characteristic timescales, witness the transition both through their dependence on the interaction strength and through the scaling with the system size. Since the QFI also sets the ultimate bound for the precision of parameter estimation, it provides a metrological perspective on the characterization of entanglement dynamics in many-body systems. Here we show that quantum ergodic dynamics allows for a much faster production of metrologically useful states.
A numerical method, suitable for the simulation of the time evolution of quantum spin models of arbitrary lattice dimension, is presented. The method combines sampling of the Wigner function with evolution equations obtained from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Going to higher orders of the BBGKY hierarchy allows for a systematic refinement of the method. Quantum correlations are treated through both, the Wigner function sampling and the BBGKY evolution, bringing about highly accurate estimates of correlation functions. The method is particularly suitable for long-range interacting systems, and we demonstrate its power by comparing with exact results as well as other numerical methods. As an application we compute spin squeezing in a two-dimensional lattice with power-law interactions and a transverse field, which should be accessible in future ion trap experiments.
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