与叠后地震数据相比,叠前地震数据包含有更多的反映地下地层特征的信息,利用AVO(Amplitude Versus Offset,振幅随偏移距的变化)信息通过求解Zoeppritz方程的近似公式,叠前反演可直接得到反映地下岩石特征的弹性参数——密度、纵波速度...与叠后地震数据相比,叠前地震数据包含有更多的反映地下地层特征的信息,利用AVO(Amplitude Versus Offset,振幅随偏移距的变化)信息通过求解Zoeppritz方程的近似公式,叠前反演可直接得到反映地下岩石特征的弹性参数——密度、纵波速度和横波速度.从本质上讲,叠前地震反演是非线性的,但目前多采用线性近似方法求解,降低了地震反演的精度.本文研究基于Aki-Richards近似公式的非线性叠前反演方法,分析了引起弹性参数非线性反演误差的因素,提出了反向加权系数的方法以均衡各反演参数的系数所引起的响应差异,并把具有较强的非线性搜索能力、能够更好地求取全局最优解的量子蒙特卡罗方法引入到叠前三参数非线性反演,改善了叠前反演的精度.理论和实例试算表明:该方法计算精度较高、稳定性较好.展开更多
Using exact quantum Monte Carlo method, we examine the recent novel electronic states seen in magicangle graphene superlattices. From the Hubbard model on a double-layer honeycomb lattice with a rotation angle θ=1:08...Using exact quantum Monte Carlo method, we examine the recent novel electronic states seen in magicangle graphene superlattices. From the Hubbard model on a double-layer honeycomb lattice with a rotation angle θ=1:08°, we reveal that an antiferromagnetically ordered Mott insulator emerges beyond a critical U_c at half filling, and with a small doping, the pairing with d+id symmetry dominates over other pairings at low temperature. The effective d+id pairing interaction strongly increases as the on-site Coulomb interaction increases, indicating that the superconductivity is driven by electron-electron correlation. Our non-biased numerical results demonstrate that the twisted bilayer graphene shares the similar superconducting mechanism of high temperature superconductors, which is a new and ideal platform for further investigating the strongly correlated phenomena.展开更多
We utilize the Hirsch-Fye quantum Monte Carlo method to investigate the local moment formation of a magnetic impurity in a Bernal-stacked bilayer honeycomb lattice. A tight-binding model with the two most significant ...We utilize the Hirsch-Fye quantum Monte Carlo method to investigate the local moment formation of a magnetic impurity in a Bernal-stacked bilayer honeycomb lattice. A tight-binding model with the two most significant inter-layer hoppings, tl between pairs of dimer sites and t3 between pairs of non-dimer sites, is used to describe the kinetic energy of the system. The local moment formed shows an asymmetric response to the inter-layer hoppings depending on which sublattice the impurity is coupled to. In the dimer and non-dimer couplings, the effects of t1 and t3 onto the local moment are quite opposite. When tuning the local moment, this asymmetric response is observed in a wide parameter range. This asymmetric response is also discussed by the computations of spectral densities, as well as correlation functions between the magnetic impurity and the conduction electrons.展开更多
The major difficulty for the Feynman Path Integral Monte Carlo (PIMC) simulations of the quantum systems of particles is the so called “sign problem”, arising due to the fast oscillations of the path integral integr...The major difficulty for the Feynman Path Integral Monte Carlo (PIMC) simulations of the quantum systems of particles is the so called “sign problem”, arising due to the fast oscillations of the path integral integrand depending on the complex-valued action. Our aim is to find universal techniques being able to solve this problem. The new method combines the basic ideas of the Metropolis and Hasting algorithms and is based on the Picard-Lefschetz theory and complex-valued version of Morse theory. The basic idea is to choose the Lefschetz thimbles as manifolds approaching the saddle point of the integrand. On this thimble the imaginary part of the complex-valued action remains constant. As a result the integrand on each thimble does not oscillate, so the “sign problem” disappears and the integral can be calculated much more effectively. The developed approach allows also finding saddle points in the complexified space of path integral integration. Some simple test calculations and comparisons with available analytical results have been carried out.展开更多
Quantum interference and exchange statistical effects can affect the momentum distribution functions making them non-Maxwellian. Such effects may be important in studies of kinetic properties of matter at low temperat...Quantum interference and exchange statistical effects can affect the momentum distribution functions making them non-Maxwellian. Such effects may be important in studies of kinetic properties of matter at low temperatures and under extreme conditions. In this work we have generalized the path integral representation for Wigner function to strongly coupled three-dimensional quantum system of particles with Boltzmann and Fermi statistics. In suggested approach the explicit expression for Wigner function was obtained in harmonic approximation and Monte Carlo method allowing numerical calculation of Wigner function, distribution functions and average quantum values has been developed. As alternative more accurate single-momentum approach and related Monte Carlo method have been developed to calculation of the distribution functions of degenerate system of interacting fermions. It allows partially overcoming the well-known sign problem for degenerate Fermi systems.展开更多
In this article, we review our recent work on quantum phase transition in two-dimensional strongly correlated fermion systems. We discuss the metal insulator transition properties of these systems by calculating the d...In this article, we review our recent work on quantum phase transition in two-dimensional strongly correlated fermion systems. We discuss the metal insulator transition properties of these systems by calculating the density of states, double occupancy, and Fermi surface evolution using a com- bination of the cellular dynamical mean-field theory （CDMFT） and the continuous-time quantum Monte Carlo algorithm. Furthermore, we explore the magnetic properties of each state by defining magnetic order parameters. Rich phase diagrams with many intriguing quantum states, including antiferromagnetic metal, paramagnetic metal, Kondo metal, and ferromagnetic insulator, were found for the two-dimensional lattices with strongly correlated fermions. We believe that our results would lead to a better understanding of the properties of real materials.展开更多
文摘与叠后地震数据相比,叠前地震数据包含有更多的反映地下地层特征的信息,利用AVO(Amplitude Versus Offset,振幅随偏移距的变化)信息通过求解Zoeppritz方程的近似公式,叠前反演可直接得到反映地下岩石特征的弹性参数——密度、纵波速度和横波速度.从本质上讲,叠前地震反演是非线性的,但目前多采用线性近似方法求解,降低了地震反演的精度.本文研究基于Aki-Richards近似公式的非线性叠前反演方法,分析了引起弹性参数非线性反演误差的因素,提出了反向加权系数的方法以均衡各反演参数的系数所引起的响应差异,并把具有较强的非线性搜索能力、能够更好地求取全局最优解的量子蒙特卡罗方法引入到叠前三参数非线性反演,改善了叠前反演的精度.理论和实例试算表明:该方法计算精度较高、稳定性较好.
基金supported by the National Natural Science Foundation of China(11374034 and 11334012)Beijing Natural Science Foundation(1192011)+1 种基金support of HSCC of Beijing Normal Universitythe Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund
文摘Using exact quantum Monte Carlo method, we examine the recent novel electronic states seen in magicangle graphene superlattices. From the Hubbard model on a double-layer honeycomb lattice with a rotation angle θ=1:08°, we reveal that an antiferromagnetically ordered Mott insulator emerges beyond a critical U_c at half filling, and with a small doping, the pairing with d+id symmetry dominates over other pairings at low temperature. The effective d+id pairing interaction strongly increases as the on-site Coulomb interaction increases, indicating that the superconductivity is driven by electron-electron correlation. Our non-biased numerical results demonstrate that the twisted bilayer graphene shares the similar superconducting mechanism of high temperature superconductors, which is a new and ideal platform for further investigating the strongly correlated phenomena.
基金Project supported by the National Natural Science Foundation of China(Grant No.11604166)the Zhejiang Open Foundation of the Most Important Subjects,China(Grant No.xkzw11609)the K.C.Wong Magna Fund in Ningbo University,China
文摘We utilize the Hirsch-Fye quantum Monte Carlo method to investigate the local moment formation of a magnetic impurity in a Bernal-stacked bilayer honeycomb lattice. A tight-binding model with the two most significant inter-layer hoppings, tl between pairs of dimer sites and t3 between pairs of non-dimer sites, is used to describe the kinetic energy of the system. The local moment formed shows an asymmetric response to the inter-layer hoppings depending on which sublattice the impurity is coupled to. In the dimer and non-dimer couplings, the effects of t1 and t3 onto the local moment are quite opposite. When tuning the local moment, this asymmetric response is observed in a wide parameter range. This asymmetric response is also discussed by the computations of spectral densities, as well as correlation functions between the magnetic impurity and the conduction electrons.
文摘The major difficulty for the Feynman Path Integral Monte Carlo (PIMC) simulations of the quantum systems of particles is the so called “sign problem”, arising due to the fast oscillations of the path integral integrand depending on the complex-valued action. Our aim is to find universal techniques being able to solve this problem. The new method combines the basic ideas of the Metropolis and Hasting algorithms and is based on the Picard-Lefschetz theory and complex-valued version of Morse theory. The basic idea is to choose the Lefschetz thimbles as manifolds approaching the saddle point of the integrand. On this thimble the imaginary part of the complex-valued action remains constant. As a result the integrand on each thimble does not oscillate, so the “sign problem” disappears and the integral can be calculated much more effectively. The developed approach allows also finding saddle points in the complexified space of path integral integration. Some simple test calculations and comparisons with available analytical results have been carried out.
文摘Quantum interference and exchange statistical effects can affect the momentum distribution functions making them non-Maxwellian. Such effects may be important in studies of kinetic properties of matter at low temperatures and under extreme conditions. In this work we have generalized the path integral representation for Wigner function to strongly coupled three-dimensional quantum system of particles with Boltzmann and Fermi statistics. In suggested approach the explicit expression for Wigner function was obtained in harmonic approximation and Monte Carlo method allowing numerical calculation of Wigner function, distribution functions and average quantum values has been developed. As alternative more accurate single-momentum approach and related Monte Carlo method have been developed to calculation of the distribution functions of degenerate system of interacting fermions. It allows partially overcoming the well-known sign problem for degenerate Fermi systems.
基金I am so grateful for the great contribu- tions and beneficial communications from Yao-Hua Chen, Hai-Di Liu, and Heng-Fu Lin while I am preparing this review paper. This work was supported by the National Science Foundation of China （Grant Nos. 11174169, 11234007, and 51471093）.
文摘In this article, we review our recent work on quantum phase transition in two-dimensional strongly correlated fermion systems. We discuss the metal insulator transition properties of these systems by calculating the density of states, double occupancy, and Fermi surface evolution using a com- bination of the cellular dynamical mean-field theory （CDMFT） and the continuous-time quantum Monte Carlo algorithm. Furthermore, we explore the magnetic properties of each state by defining magnetic order parameters. Rich phase diagrams with many intriguing quantum states, including antiferromagnetic metal, paramagnetic metal, Kondo metal, and ferromagnetic insulator, were found for the two-dimensional lattices with strongly correlated fermions. We believe that our results would lead to a better understanding of the properties of real materials.
