The on-shell renormalization scheme for electroweak theory is well studied in the standard model (SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model (MSSM) is still...The on-shell renormalization scheme for electroweak theory is well studied in the standard model (SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model (MSSM) is still unknown. In the MSSM, we study the on-shell scheme for three vertexes: with virtual SUSY particles (chargino, sneutrino, neutralino and slepton) at one-loop order. Instead of the amplitude of a single triangle diagram, the sum of the amplitude of triangle diagrams belonging to one suit can be renormalized in the on-shell scheme. One suit points out that the internal virtual particles are consistent. The zero-momentum scheme is also used for the renormalization. The two schemes can make the renormalized results decoupled, and in the MSSM some of the special characters of the on-shell scheme are shown. This work is propitious in completing the on-shell renormalization scheme in the MSSM.展开更多
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 renorma...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.展开更多
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 combinatorial...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.展开更多
Renormalization group theory applied to turbulence will be reviewed in this article.Techniques associated are used for analyzing thermally-induced turbulence.Transport properties such as effective viscosity and therma...Renormalization group theory applied to turbulence will be reviewed in this article.Techniques associated are used for analyzing thermally-induced turbulence.Transport properties such as effective viscosity and thermal diffusivity are derived.展开更多
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 microstru...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.展开更多
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 introduc...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.展开更多
With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Ya...With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.展开更多
We study the relation between renormalization of the chemical potential due to multiphonon effects at the surface of Be(0001) and doping by solving the strong-coupling self-consistent equations of a two-dimensional...We study the relation between renormalization of the chemical potential due to multiphonon effects at the surface of Be(0001) and doping by solving the strong-coupling self-consistent equations of a two-dimensional(2D) electron-phonon interaction system.We present the quasiparticle dispersions and inverse lifetimes of a 2D electron system interacting with Einstein phonons under the different dopings(corresponding to chemical potentials).We find that the effect of electron-phonon interaction on electron structure is strongest at the half filling,but it has no effect on the chemical potential.However,the chemical potential shows distinct renormalization effects away from half filling due to the electron-phonon interaction.展开更多
A one step real space renormalization group(RSRG)transformation is used to study the ferromagnetic(FM)Potts model on the two dimemsional (2D) octagonal quasi periodic tiling(OQT). The critical exponents of the ...A one step real space renormalization group(RSRG)transformation is used to study the ferromagnetic(FM)Potts model on the two dimemsional (2D) octagonal quasi periodic tiling(OQT). The critical exponents of the correlation length in the q =1,2,3,4 cases and the crtitical surface of the Ising model are obtained. The results are discussed by comparing with previous results on the OQT and the square lattice(SQL).展开更多
This paper presents the application of the renormalization group (RG) methods to the delayed differential equation. By analyzing the Mathieu equation with time delay feedback, we get the amplitude and phase equation...This paper presents the application of the renormalization group (RG) methods to the delayed differential equation. By analyzing the Mathieu equation with time delay feedback, we get the amplitude and phase equations, and then obtain the approximate solutions by solving the corresponding RG equations. It shows that the approximate solutions obtained from the RG method are superior to those from the conventionally perturbation methods.展开更多
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 corr...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.展开更多
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-dime...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.展开更多
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...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.展开更多
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 ...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.展开更多
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 ...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.展开更多
Renormalization group recursions are obtained by virtue of the variational cumulant expansion method. Good qualitative estimates are obtained for the d=2 square Ising system.
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 re...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.展开更多
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 improv...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.展开更多
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 th...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 R<sub>1</sub> and R<sub>2 </sub>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.展开更多
基金Supported by National Natural Science Foundation (11047002, 10975027)Natural Science Foundation of Hebei Province in China (A2011201118)
文摘The on-shell renormalization scheme for electroweak theory is well studied in the standard model (SM), but a consistent on-shell renormalization scheme for the minimal supersymmetric standard model (MSSM) is still unknown. In the MSSM, we study the on-shell scheme for three vertexes: with virtual SUSY particles (chargino, sneutrino, neutralino and slepton) at one-loop order. Instead of the amplitude of a single triangle diagram, the sum of the amplitude of triangle diagrams belonging to one suit can be renormalized in the on-shell scheme. One suit points out that the internal virtual particles are consistent. The zero-momentum scheme is also used for the renormalization. The two schemes can make the renormalized results decoupled, and in the MSSM some of the special characters of the on-shell scheme are shown. This work is propitious in completing the on-shell renormalization scheme in the MSSM.
基金Project support from the National Natural Science Foundation of China(Grant No.11604254)the Natural Science Foundation of Shaanxi ProvinceChina(Grant No.2019JQ-240)。
文摘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.
文摘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.
文摘Renormalization group theory applied to turbulence will be reviewed in this article.Techniques associated are used for analyzing thermally-induced turbulence.Transport properties such as effective viscosity and thermal diffusivity are derived.
基金the National Natural Science Foundation of China(Grant No.51534002)the Special Funds for Technological Innovation and Entrepreneurship of China Coal Science and Engineering Group Co.Ltd.(2018-TDMS011)。
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (10872192)
文摘With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10574063)
文摘We study the relation between renormalization of the chemical potential due to multiphonon effects at the surface of Be(0001) and doping by solving the strong-coupling self-consistent equations of a two-dimensional(2D) electron-phonon interaction system.We present the quasiparticle dispersions and inverse lifetimes of a 2D electron system interacting with Einstein phonons under the different dopings(corresponding to chemical potentials).We find that the effect of electron-phonon interaction on electron structure is strongest at the half filling,but it has no effect on the chemical potential.However,the chemical potential shows distinct renormalization effects away from half filling due to the electron-phonon interaction.
文摘A one step real space renormalization group(RSRG)transformation is used to study the ferromagnetic(FM)Potts model on the two dimemsional (2D) octagonal quasi periodic tiling(OQT). The critical exponents of the correlation length in the q =1,2,3,4 cases and the crtitical surface of the Ising model are obtained. The results are discussed by comparing with previous results on the OQT and the square lattice(SQL).
文摘This paper presents the application of the renormalization group (RG) methods to the delayed differential equation. By analyzing the Mathieu equation with time delay feedback, we get the amplitude and phase equations, and then obtain the approximate solutions by solving the corresponding RG equations. It shows that the approximate solutions obtained from the RG method are superior to those from the conventionally perturbation methods.
文摘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.
文摘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.
文摘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.
文摘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.
基金The project supported by the National Natural Science Foundation of China
文摘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.
文摘Renormalization group recursions are obtained by virtue of the variational cumulant expansion method. Good qualitative estimates are obtained for the d=2 square Ising system.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11834005,and 11904145)the Program for Changjiang Scholars and Innovative Research Team in Universities,China(Grant No.IRT-16R35).
文摘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.
文摘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 R<sub>1</sub> and R<sub>2 </sub>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.