The efficiency of the calculation of Green＇s function （GF） for nano-devices is very important because the calculation is often needed to be repeated countlessly. We present a set of efficient algorithms for the num...The efficiency of the calculation of Green＇s function （GF） for nano-devices is very important because the calculation is often needed to be repeated countlessly. We present a set of efficient algorithms for the numerical calculation of GF for devices with arbitrary shapes and multi-terminal configurations. These algorithms can be used to calculate the specified blocks related to the transmission, the diagonals needed by the local density of states calculation, and the full matrix of GF, to meet different calculation levels. In addition, the algorithms for the non-equilibrium occupation and current flow are also given. All these algorithms are described using the basic theory of GF, based on a new partition strategy of the computational area. We apply these algorithms to the tight-binding graphene lattice to manifest their stability and efficiency. We also discuss the physics of the calculation results.展开更多
Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results d...Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10904040 and 10974058)
文摘The efficiency of the calculation of Green＇s function （GF） for nano-devices is very important because the calculation is often needed to be repeated countlessly. We present a set of efficient algorithms for the numerical calculation of GF for devices with arbitrary shapes and multi-terminal configurations. These algorithms can be used to calculate the specified blocks related to the transmission, the diagonals needed by the local density of states calculation, and the full matrix of GF, to meet different calculation levels. In addition, the algorithms for the non-equilibrium occupation and current flow are also given. All these algorithms are described using the basic theory of GF, based on a new partition strategy of the computational area. We apply these algorithms to the tight-binding graphene lattice to manifest their stability and efficiency. We also discuss the physics of the calculation results.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB921704)the National Natural Science Foundation of China(Grant No.11374362)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.15XNLQ03)
文摘Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.
