First-principles study of the bandgap renormalization and optical property ofβ-LiGaO_(2)

Theβ-LiGaO_(2)with an orthorhombic wurtzite-derived structure is a candidate ultrawide direct-bandgap semiconductor.In this work,using the non-adiabatic Allen-Heine-Cardona approach,we investigate the bandgap renormalization arising from electron-phonon coupling.We find a sizable zero-point motion correction of-0.362 eV to the gap atΓ,which is dominated by the contributions of long-wavelength longitudinal optical phonons.The bandgap ofβ-LiGaO_(2)decreases monotonically with increasing temperature.We investigate the optical spectra by comparing the model Bethe-Salpether equation method with the independent-particle approximation.The calculated optical spectra including electron-hole interactions exhibit strong excitonic effects,in qualitative agreement with the experiment.The contributing interband transitions and the binding energy for the excitonic states are analyzed.

Pacman Renormalization in Siegel Parameters of Bounded Type

A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.

QCD One-Loop Effective Coupling Constant and Quark Mass Given in a Mass-Dependent Renormalization

The QCD one-loop renormalization is restudied in a mass-dependent subtraction scheme in which the quark mass is not set to vanish and the renormalization point is chosen to be an arbitrary time-like momentum. The correctness of the subtraction is ensured by the Ward identities which are respected in all the processes of subtraction.By considering the mass effect, the effective coupling constant and the effective quark masses derived by solving the renormalization group equations are given in improved expressions which are different from the previous results.PACS numbers: 11.10.Gh, 11.10.Hi, 12.38.-t, 12.38.

Memory,Time and Technique Aspects of Density Matrix Renormalization Group Method

We present the memory size,computational time,and technique aspects of density matrix renormalization group (DMRG) algorithm.We show how to estimate the memory size and computational time before starting a large scale DMRG calculation.We propose an implementation of the Hamiltonian wavefunction multiplication and a wavefunction initialization in DMRG with block matrix data structure.One-dimensional Heisenberg model is used to illustrate our study.

Real-Space Renormalization Group Approach of the Potts Model on the Octagonal Quasi-Periodic Tiling

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The Homotopy Perturbation Renormalization Group Method to Solve the WKB Problem with Turn Points

In this paper,we give the homotopy perturbation renormalization group method,this is a new method for turning point problem.Using this method,the independent variables are introduced by transformation without introducing new related variables and no matching is needed.The WKB approximation method problem can be solved.

Study on the critical stress threshold of weakly cemented sandstone damage based on the renormalization group method

During the microstructural analysis of weakly cemented sandstone,the granule components and ductile structural parts of the sandstone are typically generalized.Considering the contact between granules in the microstructure of weakly cemented sandstone,three basic units can be determined:regular tetrahedra,regular hexahedra,and regular octahedra.Renormalization group models with granule-and pore-centered weakly cemented sandstone were established,and,according to the renormalization group transformation rule,the critical stress threshold of damage was calculated.The results show that the renormalization model using regular octahedra as the basic units has the highest critical stress threshold.The threshold obtained by iterative calculations of the granule-centered model is smaller than that obtained by the pore-centered model.The granule-centered calculation provides the lower limit(18.12%),and the pore-centered model provides the upper limit(36.36%).Within this range,the weakly cemented sandstone is in a phase-like critical state.That is,the state of granule aggregation transforms from continuous to discrete.In the relative stress range of 18.12%-36.36%,the weakly cemented sandstone exhibits an increased proportion of high-frequency signals(by 83.3%)and a decreased proportion of low-frequency signals(by 23.6%).The renormalization calculation results for weakly cemented sandstone explain the high-low frequency conversion of acoustic emission signals during loading.The research reported in this paper has important significance for elucidating the damage mechanism of weakly cemented sandstone.

Real-space parallel density matrix renormalization group with adaptive boundaries

We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.

Improved hybrid parallel strategy for density matrix renormalization group method

We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.

Renormalization: single-photon processes of two-level system in free space

The investigation on quantum radar requires accurate computation of the state vectors of the single-photon processes of the two-level system in free space. However, the traditional Weisskopf-Wigner(W-W) theory fails to deal with those processes other than spontaneous emission. To solve this problem, we provide a new method based on the renormalization theory. We evaluate the renormalized time-ordered Green functions associated with the single-photon processes, and relate them to the corresponding state vectors. It is found that the ultraviolet divergences generated by the Lamb shift and higher-order interactions can be systematically subtracted in the state vectors. The discussions on spontaneous emission and single-photon absorption are then presented to illustrate the proposed method. For spontaneous emission, we obtain the same results of the W-W theory. For single-photon absorption where W-W theory fails, we find that the two-level electric dipole first gets excited rapidly and then decays exponentially, and that the efficiency of the single-photon absorption declines as the bandwidth of the incident photon becomes narrow. The proposed method can improve the investigation on quantum radar.

A Renormalizable Theory of Quantum Gravity: Renormalization Proof of the Gauge Theory of Volume Preserving Diffeomorphisms

Inertial and gravitational mass or energy momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The gauge-fixed action and the path integral measure occurring in the generating functional for the quantum Green functions of the theory are shown to obey a BRST-type symmetry. The related Zinn-Justin-type equation restricting the corresponding quantum effective action is established. This equation limits the infinite parts of the quantum effective action to have the same form as the gauge-fixed Lagrangian of the theory proving its spacetime renormalizability. The inner space integrals occurring in the quantum effective action which are divergent due to the gauge group’s infinite volume are shown to be regularizable in a way consistent with the symmetries of the theory demonstrating as a byproduct that viable quantum gauge field theories are not limited to finite-dimensional compact gauge groups as is commonly assumed.

Renormalization of the g-Boson Effects for Os Isotopes

A modified renormalization approach based on that proposed by Druce et al.is presented.The over-all agreement between the spectra calculated here and the accurate spectra is significantly improved.We also useDurce’s approach to generate the renormalized spectra.It is shown that in our microscopic study,both of the ap-proaches are very useful to the determination of several free parameters of fermion residual interactions.

Renormalization of Hierarchy and Semantic Computing

In the setting of boundedness, the renormalization acquires new meaning and implementation: it appears as generic operational protocol available for intelligent complex systems aimed towards essential non-extensive reduction of computation costs and non-extensive speeding up of computing. Another advantage of the proposed above renormalization is that, along with reduction of computation costs and speeding up of computing, it allows further hierarchical super-structuring where the same properties of speeding up the computing and reduction of computation costs hold. The fundamental novelty of that renormalization is provided by a highly non-trivial interplay between structural and functional properties.

Phase Diagrams of the Semi-Infinite Blume-Capel Model with Mixed Spins (SA = 1 and SB = 3/2) by Migdal Kadanoff Renormalization Group

We study the mixed spin-1 and spin-3/2 Blume-Capel model under crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal-Kadanoff technique. As a function of the ratio R of bulk and surface interactions and the ratios R1 and R2 of bulk and surface crystals fields on the spin-1 and spin-3/2 respectively, we have determined various types of phase diagrams. Besides second- order transition lines, first-order phase transition lines terminating at tricritical points are obtained. We found that there existed nine main types of phase diagram showing a variety of phase transitions associated with the surface, including ordinary, extraordinary, surface and special phase transitions.

No Anomaly and New Renormalization Scheme

We review the physics of chiral anomaly and show that the anomaly equation of δμJμ5 =e216π2εμνρδ FμνFρδis not connected to any physical observables. This is based on the fact that the reaction process of π0→2γ has no diver- gence at all, and the triangle diagrams with the vertex of γμγ5 describing the Z0→2γ decay do not have any di- vergences either. The recent calculated branching ratio of the Z0→2γ decay rate is found to be ГZ0→2γ/Г□2.4×10-8. Further, we discuss the anomaly equation in the Schwinger model which is known as δμJμ5=e2πεμνFμν , and prove that this anomaly equation disagrees with the exact value of the chiral charge δ5=±1 in the Schwinger vacuum. Therefore, the chiral anomaly is a spurious effect induced by the regularization. In connection with the anomaly prob- lem, we clarify the physical meaning why the self-energy of photon should not be included in the renormalization scheme. Also, we present the renormalization scheme in weak interactions without Higgs particles, and this is achieved with a new propagator of massive vector bosons, which does not give rise to any logarithmic divergences in the vertex corrections. Therefore, there is no necessity of the renormalization procedure of the vertex corrections arising from the weak vector boson propagation.

Renormalization of one-pion exchange in higher partial waves in chiral effective field theory for antinucleon-nucleon system

The renormalization of the iterated onepion exchange(OPE)has been studied in chiral effective field theory(χEFT)for the antinucleon-nucleon(NN)scattering in some partial waves(Phys.Rev.C 105,054005(2022)).In this paper,we go further for the other higher partial waves but with total angular momenta J≤3.Contact interactions are represented by a complex spherical well in the coordinate space.Changing the radius of the spherical well means changing the cutoff.We check the cutoff dependence of the phase shifts,inelasticities,and mixing angles for the partial waves and show that contact interactions are needed at leading order in channels where the singular tensor potentials of OPE are attractive.The results are compared with the energy-dependent partial-wave analysis of NN scattering data.Comparisons between our conclusions and applications of χEFT to the nucleon-nuc-leon system are also discussed.

Connectivity of the Mandelbrot set for the family of renormalization transformations

We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausdorff dimension of Julia set when it is a quasi-circle.

Dynamics of exciton energy renormalization in monolayer transition metal disulfides

Fundamental understandings on the dynamics of charge carriers and excitonic quasiparticles in semiconductors are of central importance for both many-body physics and promising optoelectronic and photonic applications.Here,we investigated the carrier dynamics and many-body interactions in two-dimensional(2D)transition metal dichalcogenides(TMDs),using monolayer WS2 as an example,by employing femtosecond broadband pump-probe spectroscopy.Three time regimes for the exciton energy renormalization are unambiguously revealed with a distinct red-blue-red shift upon above-bandgap optical excitations.We attribute the dominant physical process in the three typical regimes to free carrier screening effect,Coulombic exciton-exciton interactions and Auger photocarrier generation,respectively,which show distinct dependence on the optical excitation wavelength,pump fluences and/or lattice temperature.An intrinsic exciton radiative lifetime of about 1.2 picoseconds(ps)in monolayer WS2 is unraveled at low temperature,and surprisingly the efficient Auger nonradiative decay of both bright and dark excitons puts the system in a nonequilibrium state at the nanosecond timescale.In addition,the dynamics of trions at low temperature is observed to be significantly different from that of excitons,e.g.,a long radiative lifetime of^108.7 ps at low excitation densities and the evolution of trion energy as a function of delay times.Our findings elucidate the dynamics of excitonic quasiparticles and the intricate many-body physics in 2D semiconductors,underpinning the future development of photonics,valleytronics and optoelectronics based on 2D semiconductors.

The symmetry group of Feynman diagrams and consistency of the BPHZ renormalization scheme

We study the relation between the symmetry group of a Feynman diagram and its reduced diagrams.We then prove that the counterterms in the BPHZ renormalization scheme are consistent with adding counterterms to the interaction Hamiltonian in all cases,including that of Feynman diagrams with symmetry factors.

Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap

Electronic and optical properties of materials are affected by atomic motion through the electron–phonon interaction:not only band gaps change with temperature,but even at absolute zero temperature,zero-point motion causes band-gap renormalization.We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation.For materials with light elements,the band gap renormalization is often larger than 0.3 eV,and up to 0.7 eV.This effect cannot be ignored if accurate band gaps are sought.For infrared-active materials,global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account.They even dominate zero-point renormalization for many materials,as shown by a generalized Fröhlich model that includes multiple phonon branches,anisotropic and degenerate electronic extrema,whose range of validity is established by comparison with first-principles results.