Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single particle energy are smaller than $10^{-4}$~MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial deformed, non-axial deformed, and octupole deformed potential are provided and discussed.Comment: 18 pages, 6 figure

Matter loops corrected modified gravity in Palatini formulation

Recently, corrections to the standard Einstein-Hilbert action are proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani-Hamed: matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/R gravity and $\ln R$ gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory . On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications.Comment: 11 pages, 1 figures, References adde

The effect of asymmetry of the coil block on self-assembly in ABC coil-rod-coil triblock copolymers

Using the self-consistent field approach, the effect of asymmetry of the coil block on the microphase separation is focused in ABC coil-rod-coil triblock copolymers. For different fractions of the rod block $f_{\text B}$, some stable structures are observed, i.e., lamellae, cylinders, gyroid, and core-shell hexagonal lattice, and the phase diagrams are constructed. The calculated results show that the effect of the coil block fraction $f_{\text A}$ is dependent on $f_{\text B}$. When $f_{\text B}=0.2$, the effect of asymmetry of the coil block is similar to that of the ABC flexible triblock copolymers; When $f_{\text B}=0.4$, the self-assembly of ABC coil-rod-coil triblock copolymers behaves like rod-coil diblock copolymers under some condition. When $f_{\text B}$ continues to increase, the effect of asymmetry of the coil block reduces. For $f_{\text B}=0.4$, under the symmetrical and rather asymmetrical conditions, an increase in the interaction parameter between different components leads to different transitions between cylinders and lamellae. The results indicate some remarkable effect of the chain architecture on self-assembly, and can provide the guidance for the design and synthesis of copolymer materials.Comment: 9 pages, 3 figure

Mean-field embedding of the dual fermion approach for correlated electron systems

To reduce the rapidly growing computational cost of the dual fermion lattice calculation with increasing system size, we introduce two embedding schemes. One is the real fermion embedding, and the other is the dual fermion embedding. Our numerical tests show that the real fermion and dual fermion embedding approaches converge to essentially the same result. The application on the Anderson disorder and Hubbard models shows that these embedding algorithms converge more quickly with system size as compared to the conventional dual fermion method, for the calculation of both single-particle and two-particle quantities.Comment: 10 pages, 10 figure

Dual Fermion Method for Disordered Electronic Systems

While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual fermion approach to disordered non-interacting systems using the replica method. Results for single- and two- particle quantities show good agreement with cluster extensions of the CPA; moreover, weak localization is captured. As a natural extension of the CPA, our method presents an alternative to the existing cluster theories. It can be used in various applications, including the study of disordered interacting systems, or for the description of non-local effects in electronic structure calculations.Comment: 5 pages, 4 figure

Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory

We study the ground-state octet baryon masses and sigma terms using the covariant baryon chiral perturbation theory (ChPT) with the extended-on-mass-shell (EOMS) renormalization scheme up to next-to-next-to-next-to-leading order (N$^3$LO). By adjusting the available 19 low-energy constants (LECs), a reasonable fit of the $n_f=2+1$ lattice quantum chromodynamics (LQCD) results from the PACS-CS, LHPC, HSC, QCDSF-UKQCD and NPLQCD collaborations is achieved. Finite-volume corrections to the lattice data are calculated self-consistently. Our study shows that N$^3$LO BChPT describes better the light quark mass evolution of the lattice data than the NNLO BChPT does and the various lattice simulations seem to be consistent with each other. We also predict the pion and strangeness sigma terms of the octet baryons using the LECs determined in the fit of their masses. The predicted pion- and strangeness-nucleon sigma terms are $\sigma_{\pi N}=43(1)(6)$ MeV and $\sigma_{s N}=126(24)(54)$ MeV, respectively.Comment: 28 pages, 6 figures, minor revisions, typos corrected, version to appear in JHE

Cosmological Effects of Nonlinear Electrodynamics

It will be shown that a given realization of nonlinear electrodynamics, used as source of Einstein's equations, generates a cosmological model with interesting features, namely a phase of current cosmic acceleration, and the absence of an initial singularity, thus pointing to a way to solve two important problems in cosmology