Scaling behavior of crystalline membranes: an ϵ\epsilon-expansion approach

We study the scaling behavior of two-dimensional (2D) crystalline membranes in the flat phase by a renormalization group (RG) method and an $\epsilon$-expansion. Generalization of the problem to non-integer dimensions, necessary to control the $\epsilon$-expansion, is achieved by dimensional continuation of a well-known effective theory describing out-of-plane fluctuations coupled to phonon-mediated interactions via a scalar composite field, equivalent for small deformations to the local Gaussian curvature. The effective theory, which will be referred to as Gaussian curvature interaction (GCI) model, is equivalent to theories of elastic $D$-dimensional manifolds fluctuating in a $(D + d_{c})$-dimensional embedding space in the physical case $D = 2$ for arbitrary $d_{c}$. For $D\neq 2$, instead, the GCI model is not equivalent to a direct dimensional continuation of elastic membrane theory and it defines an alternative generalization to generic internal dimension $D$. We calculate explicitly RG functions at two-loop order and determine the exponent $\eta$ characterizing the long-wavelength scaling of correlation functions to order $\epsilon^{2}$ in an $\epsilon=(4-D)$-expansion. The self-consistent screening approximation (SCSA) for the GCI model is shown to be exact to O($\epsilon^{2}$). For $d_{c} = 1$, the O($\epsilon^{2}$) correction is suppressed by a small numerical prefactor. As a result, despite the large value of $\epsilon = 2$, extrapolation of the first and second order results to $D = 2$ leads to very close numbers, $\eta = 0.8$ and $\eta \simeq 0.795$. The calculated exponent values are close to earlier reference results obtained by non-perturbative RG, the SCSA and numerical simulations. These indications suggest that a perturbative analysis of the GCI model could provide an useful framework for accurate quantitative predictions of the scaling exponent even at $D = 2$.Comment: 15 pages, 4 figure

Dynamics of quasiparticles in graphene under intense circularly polarized light

A monolayer of graphene irradiated with circularly polarized light suggests a unique platform for surface electromagnetic wave (plasmon-polariton) manipulation. In fact, the time periodicity of the Hamiltonian leads to a geometric Aharonov-Anandan phase and results in a photovoltaic Hall effect in graphene, creating off-diagonal components of the conductivity tensor. The latter drastically changes the dispersion relation of surface plasmon-polaritons, leading to hybrid wave generation. In this paper we present a systematic and self-contained analysis of the hybrid surface waves obtained from Maxwell equations based on a microscopic formula for the conductivity. We consider a practical example of graphene sandwiched between two dielectric media and show that in the one-photon approximation there is formation of propagating hybrid surface waves. From this analysis emerges the possibility of a reliable experimental realization to study Zitterbewegung of charge carriers of graphene.Comment: 9 pages, 4 figure

Tunable electronic and magneto-optical properties of monolayer arsenene from GW approximation to large-scale tight-binding simulations

Monolayers of group VA elements have attracted great attention with the rising of black phosphorus. Here, we derive a simple tight-binding model for monolayer grey arsenic, referred as arsenene (ML-As), based on the first-principles calculations within the partially self-consistent GW0 approach. The resulting band structure derived from the six p-like orbitals coincides with the quasi-particle energy from GW0 calculations with a high accuracy. In the presence of a perpendicular magnetic field, ML-As exhibits two sets of Landau levels linear with respect to the magnetic field and level index. Our numerical calculation of the optical conductivity reveals that the obtained optical gap is very close to the GW0 value and can be effectively tuned by external magnetic field. Thus, our proposed TB model can be used for further large-scale simulations of the electronic, optical and transport properties of ML-As

Ultralong-range order in the Fermi-Hubbard model with long-range interactions

We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a $64 \times 64$ square lattice we demonstrate the existence of a novel phase, possessing an `ultralong-range' order. The fingerprint of this phase -- the density correlation function -- features a non-trivial behavior on a scale of tens of the lattice sites. We study the properties and the stability of the ultralong-range ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms

Importance of bath dynamics for decoherence in spin systems

We study the decoherence of two coupled spins that interact with a chaotic spin-bath environment. It is shown that connectivity of spins in the bath is of crucial importance for the decoherence of the central system. The previously found phenomenon of two-step decoherence (Phys. Rev. Lett. {\bf 90}, 210401 (2003)) turns out to be typical for the bath with a slow enough dynamics or no dynamics. For a generic random system with chaotic dynamics a conventional exponential relaxation to the pointer states takes place. Our results confirm a conjecture of Paz and Zurek (Phys. Rev. Lett. {\bf 82}, 5181 (1999)) that for weak enough interactions the pointer states are eigenstates of the central system.Comment: submitted to Physical Review Letter

Power-law energy level-spacing distributions in fractals

In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise linear functions. We propose that such a behaviour is a general feature of fractals, which can not be described properly by random matrix theory. Several other arguments for the power-law behaviour of the energy level-spacing distributions are proposed

On the feasibility of saltational evolution

Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations occurring simultaneously, within a single generation in one genome, and being fixed all together in the evolving population. The results indicate that, for typical, empirically observed combinations of the parameters of the evolutionary process, namely, effective population size, mutation rate, and distribution of selection coefficients of mutations, the probability of a multi-mutation leap is low, and accordingly, the contribution of such leaps is minor at best. However, we show that, taking sign epistasis into account, leaps could become an important factor of evolution in cases of substantially elevated mutation rates, such as stress-induced mutagenesis in microbes. We hypothesize that stress-induced mutagenesis is an evolvable adaptive strategy.Comment: Extended version, in particular, the section is added on non-equilibrium model of stress-induced mutagenesi

First-principles studies of water adsorption on graphene: The role of the substrate

We investigate the electronic properties of graphene upon water adsorption and study the influence of the SiO2 substrate in this context using density functional calculations. Perfect suspended graphene is rather insensitive to H2O adsorbates, as doping requires highly oriented H2O clusters. For graphene on a defective SiO2 substrate, we find a strongly different behavior: H2O adsorbates can shift the substrate's impurity bands and change their hybridization with the graphene bands. In this way, H2O can lead to doping of graphene for much lower adsorbate concentrations than for free hanged graphene. The effect depends strongly on the microscopic substrate properties.Comment: 4 pages, 3 figure