A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to exten...A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.展开更多
采用Stochastic Series Expansion(SSE)量子蒙特卡洛方法对正方晶格中自旋为1/2的反铁磁海森堡模型进行计算机模拟,给出能量、比热及均匀磁化率与温度的变化关系。结果表明:在各向同性情况下,温度约在kT/J=0.6处,比热有峰值,温度约在kT/...采用Stochastic Series Expansion(SSE)量子蒙特卡洛方法对正方晶格中自旋为1/2的反铁磁海森堡模型进行计算机模拟,给出能量、比热及均匀磁化率与温度的变化关系。结果表明:在各向同性情况下,温度约在kT/J=0.6处,比热有峰值,温度约在kT/J=1处,均匀磁化率达到饱和,且晶格大小的有限性对热力学量与温度的变化行为有一定的影响;在各向异性情况下,能量随着各向异性参数g的增加而减小,且在低温区,当g<1时,均匀磁化率随温度变化比较缓慢,当g>1时,均匀磁化率随温度降低向零指数衰减,在高温区,对不同各向异性参数g,均匀磁化率随温度变化行为趋于一致。展开更多
A differential approach for self-optimizing diffusion Monte Carlo calculation was proposed in this paper, which is a new algorithm combining three techniques such as optimizing, diffusion and correlation sampling. Thi...A differential approach for self-optimizing diffusion Monte Carlo calculation was proposed in this paper, which is a new algorithm combining three techniques such as optimizing, diffusion and correlation sampling. This method can be used to directly compute the energy differential between two system in the diffusion process, making the statistical error of calculation be reduced to Order of 10?-5 hartree, and recover about more than 80% of the correlation. We employed this approach to set up a potential energy surface of a molecule, used a “rigid move” model, and utilized Jacobi transformation to make energy calculation for two configurations of a molecule having good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with good quality can be depicted. In calculation, a technique called “post-equilibrium remaining sample” was set up firstly, which can save about 50% of computation expense. This novel algorithm was used to study the potential as molecular spectroscopy and the energy variation in chemical reactions.展开更多
The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied. For a specific regime of the parameters （tx = tp,ty 〈 0）, the exact ground-state is found analytically, which is a dimerized insulat...The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied. For a specific regime of the parameters （tx = tp,ty 〈 0）, the exact ground-state is found analytically, which is a dimerized insulator with one electron bound in each rung of the ladder. For the case tx, ty, tp 〉 0, the system is exactly studied using quantum Monte Carlo （QMC） method without a sign problem. It is found that the system is a Mott insulator for small tp and a quantum phase transition to a superfluid phase is driven by increasing tp. The critical t~ is determined precisely by a scaling analysis. Since it is possible that the Creutz ladder is realized experimentally, the theoretical results are interesting to the cold-atom experiments.展开更多
In this paper, a novel method for fixed-node quantum Monte Carlo is given. We have derived an expansion of the eigenvalue of the energy for a system and proved that the value of the energy calculated using the tradit...In this paper, a novel method for fixed-node quantum Monte Carlo is given. We have derived an expansion of the eigenvalue of the energy for a system and proved that the value of the energy calculated using the traditional fixed-node quantum Monte Carlo method is only the zero order approximation of the eigenvalue of the energy. But when using our novel method, in the case of only increasing less computing amounts (<1%), we can obtain conveniently the first order approximation, second order approximation, and so on. We have calculated the values of the zero, first and second approximation (0, 1 and 2) of the energies of 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O using this novel method. The results indicate that for 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O it needs only the second order approximation to obtain electronic correlation energy with over 97%. This demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.展开更多
In this paper we propose a novel diffusion quantum Monte Carlo algo-rithm, it is a self-optimizing and self-improving procedure. The method has been em-ployed to calculate the potential energy curve of C2. The total e...In this paper we propose a novel diffusion quantum Monte Carlo algo-rithm, it is a self-optimizing and self-improving procedure. The method has been em-ployed to calculate the potential energy curve of C2. The total energies for the X 1Σg+state of C2 were calculated at seven values of the bond length: 0. 106, 0. 111, 0. 124,0. 132, 0. 143, 0. 159 and 0. 185 nm; and a smooth potential energy curve was ob-tained, because when the self-optimizing technique is used, the statistical error decreas-es tremendously. The calculation results on the potential energy curve of C2 show thatthe self-optimizing diffusion quantum Monte Carlo method proposed in the present pa-per is successful.展开更多
In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm, which is a self-optimizing and self-improving procedure. In contrast to the previous EFNQMC method, the trial function is opti...In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm, which is a self-optimizing and self-improving procedure. In contrast to the previous EFNQMC method, the trial function is optimized synchronistically in the diffusion procedure, but not before the beginning of EFNQMC computation. In order to optimize the trial function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi-Newton and converges super linearly. We also use a novel trial function, which has correct electron-electron and electron-nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 11 A1 state of CH2, 1Ag state of C8 and the ground-states of H2, LiH, Li2, H2O, respectively. The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.展开更多
基金Project supported by the Special Foundation for State Major Basic Research Program of China （Grant No G2000035602） and the National Natural Science Foundation of China （Grant No 90307006）.
文摘A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.
文摘采用Stochastic Series Expansion(SSE)量子蒙特卡洛方法对正方晶格中自旋为1/2的反铁磁海森堡模型进行计算机模拟,给出能量、比热及均匀磁化率与温度的变化关系。结果表明:在各向同性情况下,温度约在kT/J=0.6处,比热有峰值,温度约在kT/J=1处,均匀磁化率达到饱和,且晶格大小的有限性对热力学量与温度的变化行为有一定的影响;在各向异性情况下,能量随着各向异性参数g的增加而减小,且在低温区,当g<1时,均匀磁化率随温度变化比较缓慢,当g>1时,均匀磁化率随温度降低向零指数衰减,在高温区,对不同各向异性参数g,均匀磁化率随温度变化行为趋于一致。
基金Project (No. 29773036) supperted by the National Natural Science Foundation of China.
文摘A differential approach for self-optimizing diffusion Monte Carlo calculation was proposed in this paper, which is a new algorithm combining three techniques such as optimizing, diffusion and correlation sampling. This method can be used to directly compute the energy differential between two system in the diffusion process, making the statistical error of calculation be reduced to Order of 10?-5 hartree, and recover about more than 80% of the correlation. We employed this approach to set up a potential energy surface of a molecule, used a “rigid move” model, and utilized Jacobi transformation to make energy calculation for two configurations of a molecule having good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with good quality can be depicted. In calculation, a technique called “post-equilibrium remaining sample” was set up firstly, which can save about 50% of computation expense. This novel algorithm was used to study the potential as molecular spectroscopy and the energy variation in chemical reactions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11274032,11774019,51472016,and 51672018)
文摘The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied. For a specific regime of the parameters （tx = tp,ty 〈 0）, the exact ground-state is found analytically, which is a dimerized insulator with one electron bound in each rung of the ladder. For the case tx, ty, tp 〉 0, the system is exactly studied using quantum Monte Carlo （QMC） method without a sign problem. It is found that the system is a Mott insulator for small tp and a quantum phase transition to a superfluid phase is driven by increasing tp. The critical t~ is determined precisely by a scaling analysis. Since it is possible that the Creutz ladder is realized experimentally, the theoretical results are interesting to the cold-atom experiments.
基金This research work was supported by the National Natural Science Foundation of China(No.29773036)Science Foundation of the Education Committee of Hunan.
文摘In this paper, a novel method for fixed-node quantum Monte Carlo is given. We have derived an expansion of the eigenvalue of the energy for a system and proved that the value of the energy calculated using the traditional fixed-node quantum Monte Carlo method is only the zero order approximation of the eigenvalue of the energy. But when using our novel method, in the case of only increasing less computing amounts (<1%), we can obtain conveniently the first order approximation, second order approximation, and so on. We have calculated the values of the zero, first and second approximation (0, 1 and 2) of the energies of 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O using this novel method. The results indicate that for 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O it needs only the second order approximation to obtain electronic correlation energy with over 97%. This demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.
文摘In this paper we propose a novel diffusion quantum Monte Carlo algo-rithm, it is a self-optimizing and self-improving procedure. The method has been em-ployed to calculate the potential energy curve of C2. The total energies for the X 1Σg+state of C2 were calculated at seven values of the bond length: 0. 106, 0. 111, 0. 124,0. 132, 0. 143, 0. 159 and 0. 185 nm; and a smooth potential energy curve was ob-tained, because when the self-optimizing technique is used, the statistical error decreas-es tremendously. The calculation results on the potential energy curve of C2 show thatthe self-optimizing diffusion quantum Monte Carlo method proposed in the present pa-per is successful.
文摘In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm, which is a self-optimizing and self-improving procedure. In contrast to the previous EFNQMC method, the trial function is optimized synchronistically in the diffusion procedure, but not before the beginning of EFNQMC computation. In order to optimize the trial function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi-Newton and converges super linearly. We also use a novel trial function, which has correct electron-electron and electron-nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 11 A1 state of CH2, 1Ag state of C8 and the ground-states of H2, LiH, Li2, H2O, respectively. The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.
