Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model

In this paper we consider the quantum phase transition in the Ising model in the presence of a transverse field in one, two and three dimensions from a multi-partite entanglement point of view. Using \emph{exact} numerical solutions, we are able to study such systems up to 25 qubits. The Meyer-Wallach measure of global entanglement is used to study the critical behavior of this model. The transition we consider is between a symmetric GHZ-like state to a paramagnetic product-state. We find that global entanglement serves as a good indicator of quantum phase transition with interesting scaling behavior. We use finite-size scaling to extract the critical point as well as some critical exponents for the one and two dimensional models. Our results indicate that such multi-partite measure of global entanglement shows universal features regardless of dimension $d$. Our results also provides evidence that multi-partite entanglement is better suited for the study of quantum phase transitions than the much studied bi-partite measures.Comment: 7 pages, 8 Figures. To appear in Physical Review

Scaling and Dissipation in the GOY Shell Model

This is a paper about multi-fractal scaling and dissipation in a shell model of turbulence, called the GOY model. This set of equations describes a one dimensional cascade of energy towards higher wave vectors. When the model is chaotic, the high-wave-vector velocity is a product of roughly independent multipliers, one for each logarithmic momentum shell. The appropriate tool for studying the multifractal properties of this model is shown to be the energy current on each shell rather than the velocity on each shell. Using this quantity, one can obtain better measurements of the deviations from Kolmogorov scaling (in the GOY dynamics) than were available up to now. These deviations are seen to depend upon the details of inertial-range structure of the model and hence are {\em not} universal. However, once the conserved quantities of the model are fixed to have the same scaling structure as energy and helicity, these deviations seem to depend only weakly upon the scale parameter of the model. We analyze the connection between multifractality in the velocity distribution and multifractality in the dissipation. Our arguments suggest that the connection is universal for models of this character, but the model has a different behavior from that of real turbulence. We also predict the scaling behavior of time correlations of shell-velocities, of the dissipation,Comment: Revised Versio

Dynamic Phase Transition, Universality, and Finite-size Scaling in the Two-dimensional Kinetic Ising Model in an Oscillating Field

We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multi-droplet regime where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine non-equilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations, employing finite-size scaling techniques adopted from equilibrium critical phenomena. The critical exponents, the fixed-point value of the fourth-order cumulant, and the critical order-parameter distribution all are consistent with the universality class of the two-dimensional equilibrium Ising model. We also study the cross-over from the multi-droplet to the strong-field regime, where the transition disappears

Duality in multi-channel Luttinger Liquid with local scatterer

We have devised a general scheme that reveals multiple duality relations valid for all multi-channel Luttinger Liquids. The relations are universal and should be used for establishing phase diagrams and searching for new non-trivial phases in low-dimensional strongly correlated systems. The technique developed provides universal correspondence between scaling dimensions of local perturbations in different phases. These multiple relations between scaling dimensions lead to a connection between different inter-phase boundaries on the phase diagram. The dualities, in particular, constrain phase diagram and allow predictions of emergence and observation of new phases without explicit model-dependent calculations. As an example, we demonstrate the impossibility of non-trivial phase existence for fermions coupled to phonons in one dimension

Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory

We perform Monte Carlo simulations of a supersymmetric matrix model, which is obtained by dimensional reduction of 4D SU(N) super Yang-Mills theory. The model can be considered as a four-dimensional counterpart of the IIB matrix model. We extract the space-time structure represented by the eigenvalues of bosonic matrices. In particular we compare the large N behavior of the space-time extent with the result obtained from a low energy effective theory. We measure various Wilson loop correlators which represent string amplitudes and we observe a nontrivial universal scaling in N. We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale. Comparison with the results for the bosonic case clarifies the role of supersymmetry in the large N dynamics. It does affect the multi-point correlators qualitatively, but the Eguchi-Kawai equivalence is observed even in the bosonic case.Comment: 35 pages, 17 figure

Universal scaling dynamics at non-thermal fixed points in multi-component Bose gases far from equilibrium

Far from equilibrium, comparatively little is known about the possibilities nature reserves for the structure and states of quantum many-body systems. A potential scenario is that these systems can approach a non-thermal fixed point and show universal scaling dynamics. The associated spatio-temporal self-similar evolution of correlations is characterized by universal scaling functions and scaling exponents. In this thesis, we investigate the universal scaling behavior of multi-component bosonic quantum gases from a theoretical point of view. In particular, we perform numerical simulations of spin-1 Bose gases in one and two spatial dimensions. To enable universal scaling dynamics, we prepare far-from-equilibrium initial configurations by making use of instabilities arising from a parameter quench between different phases of the spin-1 model. The subsequent universal scaling at the non-thermal fixed point is driven by the annihilation and dissolution of (quasi)topological excitations. In addition, we make analytical predictions for the non-thermal fixed point scaling of $U(N)$-symmetric models which we corroborate with numerical simulations of a $U(3)$-symmetric Bose gas in three spatial dimensions. We find that the scaling behavior at the fixed point is dominated by the conserved redistribution of collective excitations. Furthermore, we introduce prescaling as a generic feature of the evolution of a quantum many-body system towards a non-thermal fixed point. During the prescaling evolution, some well-measurable properties of spatial correlations already scale with the universal exponents of the fixed point while others still show scaling violations. We illustrate the existence of prescaling by means of numerical simulations of a three-dimensional $U(3)$-symmetric Bose gas. The research presented in this thesis contributes to a deeper understanding of universal scaling dynamics far from equilibrium. In particular, it unravels important key aspects for establishing out-of-equilibrium universality classes. Furthermore, the introduced concept of prescaling allows bridging the gap in the time evolution from the initial state to the associated non-thermal fixed point

Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments

We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched survival probability $\mathcal{P}(t)$ defined in fixed random environments is found to show multi-scaling in the critical point, meaning that $\mathcal{P}(t)=t^{-\delta}$, where the (environment and time-dependent) exponent $\delta$ has a universal limit distribution when $t\to\infty$. The limit distribution is determined by the strong disorder renormalization group method analytically in the end point of a semi-infinite lattice, where it is found to be exponential, while, in the infinite system, conjectures on its limiting behaviors for small and large $\delta$, which are based on numerical results, are formulated. By the same method, the quenched survival probability in the problem of {\it random walks in random environments} is also shown to exhibit multi-scaling with an exponential limit distribution. In addition to this, the (imaginary-time) spin-spin autocorrelation function of the {\it random transverse-field Ising chain} is found to have a form similar to that of survival probability of the contact process at the level of the renormalization approach. Consequently, a relationship between the corresponding limit distributions in the two problems can be established. Finally, the distribution of the spontaneous magnetization in this model is also discussed.Comment: 16 pages, 7 figure