[en] We study the universal scaling behavior of the entanglement entropy of critical theories in 2 + 1 dimensions. We specially consider two fermionic scale-invariant models, free massless Dirac fermions and a model of fermions with quadratic band touching, and numerically study the two-cylinder entanglement entropy of the models on the torus. We find that in both cases the entanglement entropy satisfies the area law and has the subleading term which is a scaling function of the aspect ratios of the cylindrical regions. We test the scaling of entanglement in both the free fermion models using three possible scaling functions for the subleading term derived from (a) the quasi-1D conformal field theory, (b) the bosonic quantum Lifshitz model and (c) the holographic AdS/CFT correspondence. For the later case we construct an analytic scaling function using holography, appropriate for critical theories with a gravitational dual description. We find that the subleading term in the fermionic models is well described, for a range of aspect ratios, by the scaling form derived from the quantum Lifshitz model as well as that derived using the AdS/CFT correspondence (in this case only for the Dirac model). For the case where the fermionic models are placed on a square torus we find the fit to the different scaling forms is in agreement to surprisingly high precision

[en] Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand—where the concept of linear lattice defects is not applicable—still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena. (paper)

[en] We propose an alternative approach to count the microscopic static configurations of granular packs under gravity by considering arches. This strategy obviates the problem of filtering out configurations that are not mechanically stable, opening the way for a range of granular models to be studied via ensemble theory. Following this arch-based approach, we have obtained the exact density of states for a 2D, non-interacting rigid arch model of granular assemblies. The calculated arch size distribution and volume fluctuations show qualitative agreement with realistic simulations of tapped granular beds. We have also validated our calculations by comparing them with the analytic solution for the limiting case of a quasi-1D column of frictionless disks. (paper)

[en] A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected by the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explicitly determining the bulk and boundary scattering amplitudes. The energy and quantum numbers of the low lying excitations are also derived. (paper)

[en] We analyze nonequilibrium lattice models with up–down symmetry and two absorbing states by mean-field approximations and numerical simulations in two and three dimensions. The phase diagram displays three phases: paramagnetic, ferromagnetic and absorbing. The transition line between the first two phases belongs to the Ising universality class and between the last two, to the direct percolation universality class. The two lines meet at the point describing the voter model and the size ℓ of the ferromagnetic phase vanishes with the distance ε to the voter point as ℓ ∼ ε, with possible logarithm corrections in two dimensions. (paper)

[en] We investigate the Loschmidt echo of a quantum system where a central spin is symmetrically coupled to a compass spin-chain. It is found that the Loschmidt echo and its statistical distribution are able to detect the quantum criticality of the compass spin-chain at low temperature. By applying a spin flip operation to reverse the central spin's orientation, we find the controlled spin echo and its statistical distribution can effectively reveal quantum criticality at very high temperature. Moreover, we show that the geometric phase of a central spin can be used to indicate the quantum phase transition of a compass spin-chain and obeys scaling behavior in the vicinity of a quantum phase transition. (paper)

[en] We investigate the statistics of the time taken for a system driven by recruitment to reach fixation. Our model describes a series of experiments where a population is confronted with two identical options, resulting in the system fixating on one of the options. For a specific population size, we show that the time distribution behaves like an inverse Gaussian with an exponential decay. Varying the population size reveals that the timescale of the decay depends on the population size and allows the critical population number, below which fixation occurs, to be estimated from experimental data. (paper)

[en] Resonant activation is one of the classical effects demonstrating the constructive role of noise. In resonant activation, the cooperative action of a barrier modulation process and noise lead to the optimal escape kinetics as measured by the mean first passage time. Resonant activation has been observed in versatile systems for various types of barrier modulation process and noise type. Here, we show that resonant activation is also observed in 2D and 3D systems driven by bi-variate and tri-variate α-stable noise. The strength of resonant activation is sensitive to the exact value of the noise parameters. In particular, the decrease in the stability index α results in the disappearance of the resonant activation. (paper)

[en] Diffusion of single-species particles with exclusion on a two-lane lattice is considered. The most general autonomous nearest neighbor diffusion on this two-lane lattice is introduced. The dynamics of the particle density is investigated, and the large time behavior of these one-point functions is obtained. Some special cases are investigated in more detail. (paper)

[en] Entanglement measures such as the entanglement entropy have become an indispensable tool to identify the fundamental character of ground states of interacting quantum many-body systems. For systems of interacting spin or bosonic degrees of freedom much recent progress has been made not only in the analytical description of their respective entanglement entropies but also in their numerical classification. Systems of interacting fermionic degrees of freedom, however, have proved to be more difficult to control, in particular with regard to the numerical understanding of their entanglement properties. Here we report a generalization of the replica technique for the calculation of Rényi entropies to the framework of determinantal Quantum Monte Carlo simulations—the numerical method of choice for unbiased, large-scale simulations of interacting fermionic systems. We demonstrate the strength of this approach over a recent alternative proposal based on a decomposition in free fermion Green’s functions by studying the entanglement entropy of one-dimensional Hubbard systems both at zero and finite temperatures. (paper)