Modern Physics Letters B

The non-perturbative renormalization group (NPRG), in its modern form, constitutes an efficient framework to investigate the physics of systems whose long-distance behavior is dominated by strong fluctuations that are out of reach of perturbative approaches. We present here the basic principles underlying the NPRG and illustrate its power in the context of two longstanding problems of condensed matter and soft matter physics: the nature of the phase transition occuring in frustrated magnets in three dimensions and the phase diagram of polymerized phantom membranes.

In the present paper, we present some new data supporting the existence of a spin-disordered phase in the Heisenberg model on the honeycomb lattice with antiferromagnetic interactions up to third neighbors along the line J₂ = J₃, predicted in Ref. 1. We use the Schwinger boson technique followed by a mean field decoupling and exact diagonalization for small systems to show the existence of an intermediate phase with a spin gap and short range Néel correlations in the strong quantum limit .

We summarize our theoretical findings on the ground-state phase diagram of the spin-½ XXZ chain having competing nearest-neighbor (J₁) and antiferromagnetic next-nearest-neighbor (J₂) couplings. Our study is mainly concerned with the case of ferromagnetic J₁, and the case of antiferromagnetic J₁ is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J₁/J₂ versus the XXZ anisotropy Δ: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga–Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J₁ side.

Thermodynamic properties, specific heat and magnetic susceptibility, of spin-1/2 Ising-like Heisenberg model are investigated by an exact diagonalization method for small finite size kagome- and triangular-lattices up to 18-spins. The enhancement of magnetic susceptibility from the Curie–Weiss law and the peaks-structure of specific heat, rather generally detected experimentally in triangle-based spin systems including herbertsmithite, are interpreted as an intrinsic property of triangle-based frustrated spin systems with some extent of exchange anisotropy and are inferred as owing to a quantum-classical crossover.

In order to quantify entanglement between two parts of a quantum system, one of the most used estimators is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin-1 chains.

The phase transition in frustrated spin systems is a fascinating subject in statistical physics. We show the result obtained by the Wang–Landau flat histogram Monte Carlo simulation on the phase transition in the fully frustrated simple cubic lattice with the Heisenberg spin model. The degeneracy of the ground state of this system is infinite with two continuous parameters. We find a clear first-order transition in contradiction with previous studies which have shown a second-order transition with unusual critical properties. The robustness of our calculations allows us to conclude this issue putting an end to the 20-year long uncertainty.

We study in this paper the resistivity encountered by Ising itinerant spins traveling in the so-called J₁ - J₂ frustrated simple cubic Ising lattice. For the lattice, we take into account the interactions between nearest-neighbors and next-nearest-neighbors, J₁ and J₂ respectively. Itinerant spins interact with lattice spins via a distance-dependent interaction. We also take into account an interaction between itinerant spins. The lattice is frustrated in a range of J₂ in which we show that it undergoes a very strong first-order transition. Using Monte Carlo simulation, we calculate the resistivity ρ of the itinerant spins and show that the first-order transition of the lattice causes a discontinuity of ρ.

We discuss the metal–insulator transition of the spinless fermion model with nearest-neighbor repulsion on the Kagomé lattice at 1/3- and 2/3-filling. The system is analyzed by using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the system is described by ring exchange processes. In the intermediate-coupling regime, we find that the qualitative properties of the metal–insulator transition at 1/3- and 2/3-filling are totally different reflecting the difference in the band structure near the Fermi level.

The phase diagram of one-dimensional alkaline-earth fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.

We review the infrared behavior of interacting bosons at zero temperature. After a brief discussion of the Bogoliubov approximation and the breakdown of perturbation theory due to infrared divergences, we show how the non-perturbative renormalization group enables to obtain the exact infrared behavior of the correlation functions.

We study the attractive Hubbard model in infinite spatial dimensions by means of dynamical mean-field theory with continuous-time quantum Monte Carlo simulations. Calculating the pair potential and the spectral function, we discuss the stability of the superfluid state at low temperatures. The pseudogap behavior above the critical temperature is also addressed.

A new model of cold atoms trap using a carbon nanotube is proposed. In this model, for the existence of a stable bound state of cold atom, we send a strong electromagnetic field through the carbon nanotube. This field generates an evanescent wave around the carbon nanotube and creates an effective attractive potential. The consideration of some possible boundary conditions leads to this non-trivial bound state solution. We compare also our result to the two most recent models concerning trapping of cold atoms by using a charged carbon nanotube and an optical fiber.

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low temperature region, a second-order transition occurs from a Fermi liquid to a color superfluid (CSF). In the strong attractive region, a first-order transition occurs from a CSF to a trionic state. In the high temperature region, a cross-over between a Fermi liquid and a trionic state is observed with increasing the strength of the attractive interaction. The cross-over region for fixed temperature is almost independent of filling.

We present a study of the giant piezoresistance effect in p-type silicon using full-band Monte Carlo simulation based on 30-band k.p calculation. This effect has been demonstrated experimentally in Si nanowires by He and Yang. By including the well-known strain effect on the band structure, and by introducing a law of variation of the surface potential according to the applied mechanical stress, we can reproduce this effect. This variation of surface potential modulates the depletion depth and then the conductivity of the structure. This modulation induces a strong variation of the total amount of carriers available for the conduction, which increases drastically this piezoresistive effect. This is probably the main origin of this effect, which may be used to achieve high performance MEMS sensors.

Applying the theory of nonlinear optical conductivity for an electron—phonon system, we propose a new method to obtain the line-widths of nonlinear optical conductivity in rectangular quantum wires (RQW). General analytical expressions of the nonlinear absorption power (NLAP) are obtained in the presence of an intense external field. A two-photon absorption process is taken into the result. The dependence of NLAP on the photon energy and the wire's size are numerically calculated and graphically plotted for a specific RQW. From graphs of the NLAP, we obtain line-widths as profiles of curves. The dependence of the line-widths on the temperature and parameters of a RQW are reasonable in comparison with some available theoretical and experimental results.

The influence of the bond alternation on electronic energy band structure of armchair carbon nanotubes is studied by the tight-binding approximation. It is shown that the armchair carbon nanotubes at ground state with Kekule structure open small band gap at the Fermi level. Dependence of energy band gap of armchair carbon nanotubes with Kekule structure on their radius is considered and numerically calculated. The numerical calculations are applied to the (n, n) carbon nanotubes with n = 5, 6, 7, 8.

In this paper, we present generic properties of quantum transport in mono-layer graphene. In the scheme of the Kubo–Geenwood formula, we compute the square spreading of wave packets of a given energy with is directly related to conductivity. As a first result, we compute analytically the time-dependent diffusion for pure graphene. In addition to the semi-classical term, a second term exists that is due to matrix elements of the velocity operator between electron and hole bands. This term is related to velocity fluctuations, i.e. Zitterbewegung effect. Secondly, we study numerically the quantum diffusion in graphene with simple vacancies and pair of neighboring vacancies (divacancies), that simulate schematically oxidation, hydrogenation and other functionalizations of graphene. We analyze in particular the time-dependence of the diffusion and its dependence on energy in relation with the electronic structure. We compute also the mean free path and the semi-classical value of the conductivity as a function of energy in the limit of small concentration of defects.

Spin resistivity R has been shown to result mainly from the scattering of itinerant spins with magnetic impurities and lattice spins. R is proportional to the spin–spin correlation so that its behavior is very complicated near and at the magnetic phase transition of the lattice spins. For the time being there are many new experimental data on the spin resistivity going from semiconductors to superconductors. Depending on materials, various behaviors have been observed. There is however no theory so far which gives a unified mechanism for the spin resistivity in magnetic materials. Recently, we have shown Monte Carlo results for different systems. We found that the spin resistivity is very different from one material to another. In this paper, we show for the first time how the dynamic relaxation time of the lattice spins affects the resistivity of itinerant spins observed in Monte Carlo simulation.

Using the statistical moment method (SMM), the temperature and pressure dependences of thermodynamic quantities of zinc-blende-type semiconductors have been investigated. The analytical expressions of the nearest-neighbor distances, the change of volumes and the mean-square atomic displacements (MSDs) have been derived. Numerical calculations have been performed for a series of zinc-blende-type semiconductors: GaAs, GaP, GaSb, InAs, InP and InSb. The agreement between our calculations and both earlier other theoretical results and experimental data is a support for our new theory in investigating the temperature and pressure dependences of thermodynamic quantities of semiconductors.

In this paper, we review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the usual case of photon quantum optics. Electron quantum optics aims at preparing, manipulating and measuring coherent single electron excitations propagating in ballistic conductors such as the edge channels of a 2DEG in the integer quantum Hall regime. Because of the Fermi statistics and the presence of strong interactions, electron quantum optics exhibits new features compared to the usual case of photon quantum optics. In particular, it provides a natural playground to understand decoherence and relaxation effects in quantum transport.

This note discusses the residual decoherence for a class of topologically protected qubits realized as small Josephson junction arrays. For static noise, such circuits present a decoherence rate which is exponentially small in the system size. However, in the presence of a dynamical coupling to an external bath, this length has to remain small enough so that no irreversible real transition to excited states can occur. When this condition is not satisfied, the rate of such transitions is computed through a generalization of the Fermi golden rule formula, adapted to this particular class of systems, which is derived here.

Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction — essential for a well-controllable two-qubit gate — is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the presence of spin-orbit interactions, and extract the leading correction to the block entanglement scaling due to these interactions.

The electrophonon resonance (EPR) effect in doped semiconductor superlattices (DSSL) are investigated by using the quantum kinetic equation (QKE) for electrons to obtain the general analytic expression for optical absorption coefficient. We also obtain an EPR condition as a function of the photon energy and plasma energy. In particular, anomalous behaviors of the EPR effect such as the splitting of EPR peaks for incident photon energy or plasma energy are discussed. This raises a possibility of detecting electric subbands in DSSLs experimentally by utilizing EPR effects.

We have investigated the diffusion and ionic conductivity of the cubic ceria CeO₂ using the statistical moment method (SMM) in the statistical physics. The activation energy, diffusion coefficient, pre-exponential factor and ionic conductivity are derived in closed analytic forms. The SMM calculations are performed by using the Buckingham potential for the cubic ceria. The effects of the three different potential parameter sets of the Buckingham potential and influence of dipole polarization effects on activation energy, diffusion coefficient and ionic conductivity for CeO₂ are also investigated. The present analytical formulas including the anharmonic effects of the lattice vibrations give the predicted values of these quantities, which are comparable to those of the experimental values.

Patterning ridges on the surface of microchannels has been found to be a viable strategy to induce mixing in straight channels, despite their characteristically small Reynolds numbers. In order to identify the fundamental characteristics of the advection process, we evaluate the time evolution of the Rényi entropy associated with the spatial distribution of tracers carried by an incompressible fluid moving through such channels. It is found that independent of the channel surface geometry and of the Reynolds number, the time evolution of the Rényi distributive entropy follows a universal behavior described by a logarithmic increase with time, with a slope close to unity. On the other hand, an analysis of the Shannon mixing entropy evaluated from the time evolution of the position of two tracer species moving through the channel, reveals a cross–over between two different mixing mechanisms: one dominated by the stretching of the interface between the flow regions containing different tracers, and the other dominated by chaotic mixing induced by counter-rotating transversal flows.

The bacterial reaction center couples light-induced electron transfer via a tightly bound ubiquinone (Q_A) to a mobile ubiquinone (Q_B). Based on the electron transfer theory by Marcus, we have investigated the rate of charge recombination reactions from Rhodopseudomonas viridis and Rhodobacter sphaeroides, by mean of finding an approximation formula. The results obtained are verified for not only at high and low temperature as the previous works but also at the medium temperature range.

Movement of different strains in Drosophila melanogaster was continuously observed by using computer interfacing techniques and was analyzed by permutation entropy (PE) after exposure to toxic chemicals, toluene (0.1 mg/m³) and formaldehyde (0.01 mg/m³). The PE values based on one-dimensional time series position (vertical) data were variable according to internal constraint (i.e. strains) and accordingly increased in response to external constraint (i.e. chemicals) by reflecting diversity in movement patterns from both normal and intoxicated states. Cross-correlation function revealed temporal associations between the PE values and between the component movement patterns in different chemicals and strains through the period of intoxication. The entropy based on the order of position data could be a useful means for complexity measure in behavioral changes and for monitoring the impact of stressors in environment.

Revealing biological responses of organisms in responding to environmental stressors is the critical issue in contemporary ecological sciences. Markov processes in behavioral data were unraveled by utilizing the hidden Markov model (HMM). Individual organisms of daphnia (Daphnia magna) and zebrafish (Danio rerio) were exposed to diazinon at low concentrations. The transition probability matrix (TPM) and the emission probability matrix (EPM) were accordingly estimated by training with the HMM and were verified before and after the treatments with 10^-6 tolerance in 10³ iterations. Structured property in behavioral changes was accordingly revealed to characterize dynamic processes in movement patterns. Parameters and sequences produced through the HMM training could be a suitable means of monitoring toxic chemicals in environment.

Using the simple EPB model¹ of DNA (the combined model of the pendulum model of Englander,² and Peyrard–Bishop microscopic model³), we propose a bio (DNA) time measured by EPB pendulum. We have shown that the effective bio time has a thermodynamic origin which equals the ordinary (real) time in the range of room-body temperature. Furthermore, it flows slower at low temperature and much faster near the DNA melting phase transition temperature than real time.

Blood circulating efficiently inside the veins and arteries, provides essential nutrients and oxygen to tissues and organs in the entire body. To highlight the fundamental properties of blood and gain insight into the regularizing effect of various formulations, we need to develop mathematical models. In order to do this, first we present the polymer dynamics in terms of an ensemble of Hookean dumbbells with Brownian configuration fields to derive the orientation stress tensor. Then, we describe the continuity and the momentum equations for time-dependent incompressible flow and the Oldroyd-B model. Finally, we present our numerical analysis of the model and give the effect of the orientation stress tensor in a blood vessel. The development of mathematical models and numerical procedures for the approximation of the blood specific flow equations have enabled us to understand the complex behaviors of blood flows inside the vessel.