Quantum Impurity Models with Coupled Cluster Method

We investigate the ground-state properties of the Anderson single impurity model （finite Coulomb impurity repulsion） with the Coupled Cluster Method. We consider different CCM reference states and approximation schemes and make comparison with exact Green＇s function results for the non-interacting model and with Brillouin-Wigner perturbation theory for the full interacting model. Our results show that coupled cluster techniques are well suited to quantum impurity problems.     

Quantum heat engine cycle working with a strongly correlated electron system

A new model of a quantum heat engine(QHE) cycle is established,in which the working substance consists of an interacting electrons system.One of our purposes is to test the validity of the second law of thermodynamics by this model,which is more general than the spin-1/2 antiferromagnetic Heisenberg model since it would recover the spin model when the on-site Coulomb interaction U is strong enough.On the basis of quantum mechanics and the first law of thermodynamics,we show no violation of the second law of thermodynamics during the cycle.We further study the performance characteristics of the cycle by investigating in detail the optimal relations of efficiency and dimensionless power output.We find that the efficiency of our engine can be expressed as η = 1 - t22/t12 in the large-U limit,which is valid even for a four sites QHE.     

Weakly Coupled Three-Layer Quantum Dot with a Charged Impurity in Magnetic Field

The states of a weakly coupled 3-quantum-dot system with an external charged impurity located on the z-axis are studied in a magnetic field. The evolutions of the true ground state with the magnetic field B are obtained for various impurity cases. It is found that the negative charge impurity would promote the phase transition of the true ground state.     

Coupled Cluster Method Calculations of Quantum Magnets with Spins of General Spin Quantum Number

We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, s. This new general-s formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic XXZ models and for the one-dimensional spin-half/spin-one ferrimagnetic XXZ model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalization group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetization of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at =1. By contrast, extrapolated CCM results for the sublattice magnetization of the spin-one antiferromagnet using this same scheme are seen to go to zero at 1.2, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetizations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of , up to and including the Heisenberg point at =1.     

Effects of Impurity on the Ground—State Transitions of a Quantum Dot in Strong Magnetic Field

The low-lying spectra of parabolic quantum dots with or without an impurity at the center are investigated.While it has been known that the electron-electron interaction leads to ground-state transitions on magic values of angular momentum in a magnetic field.We show,in this paper,that the implantation of an impurity ion at the center can either enhance or suppress such transitions,depending on whether it is an acceptor or a donor ion.     

在磁场作用下含有杂质的半导体量子环中电子的能级

由于量子环特殊的结构,我们尝试过不少方法,发现一般传统方法很难求解薛定谔方程,故很难求出它的波函数和能级。国内外很多学者从事这方面的研究,但发表的文献非常少。有必要寻找一些新的方法从事这方面的研究工作,本文中采用了B样条函数近似拟合波函数的方法,计算了一个在谐振子束缚势和磁场作用下含有杂质的二维量子环中的电子能级。研究了电子能级随磁场强度、束缚势的变化关系以及电子能级与量子环半径的关系。我们发现电子能级随磁场强度、束缚势强度的增强而增强;每一个能级都有一个最小值在特定的量子环半径上,并且随着能级的增加,最小值的位置向半径大的方向偏移。     

氮化物抛物量子阱中类氢杂质态能量

采用变分方法研究氮化物抛物量子阱(GaN/Al_xGa_1-xN)材料中类氢杂质态的能级,给出基态能量、第一激发态能量、结合能和跃迁能量等物理量随抛物量子阱宽度变化的函数关系.研究结果表明,基态能量、第一激发态能量、基态结合能和1s→2p±跃迁能量随着阱宽L的增大而减小,最后接近于GaN中3D值.GaN/Al_0.3Ga_0.7N抛物量子阱对杂质态的束缚程度比GaAs/Al_0.3Ga_0.7As抛物量子阱强,因此,在GaN/Al_0.3-Ga_0.7N抛物量子阱中束缚于杂质中心处的电子比在GaAs/Al_0.3Ga_0.7As抛物量子阱中束缚于杂质中心处的电子稳定.     

量子棒中强耦合杂质束缚极化子的振动频率

给出了具有椭球边界量子棒经坐标变换成球形边界的哈密顿量。采用线性组合算符和幺正变换的方法研究了在非均匀抛物限制势下量子棒中强耦合杂质束缚极化子的性质。导出了量子棒中强耦合杂质束缚极化子的振动频率和声子平均数随库仑束缚势、电子-声子耦合强度、椭球的纵横比和量子棒的横向和纵向有效受限长度的变化关系。数值计算结果表明:振动频率和声子平均数随电子-声子耦合强度和库仑束缚势的增强而增加,随量子棒的横向和纵向有效受限长度和椭球的纵横比的减小而增大。表现出量子棒的奇特的量子尺寸限制效应。     

Implementation of LDA + Gutzwiller with Newton's method

In order to calculate the electronic structure of correlated materials, we propose implementation of the LDA+Gutzwiller method with Newton's method. The self-consistence process, efficiency and convergence of calculation are improved dramatically by using Newton's method with golden section search and other improvement approaches.We compare the calculated results by applying the previous linear mix method and Newton's method. We have applied our code to study the electronic structure of several typical strong correlated materials, including SrVO_3, LaCoO_3, and La_2O_3Fe_2Se_2. Our results fit quite well with the previous studies.     

Quantum phase transition and Coulomb blockade effect in triangular quantum dots with interdot capacitive and tunnel couplings

The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method.We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t.For small t,three dots form a local spin doublet.As t increases,due to the competition between V and t,there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet.When t is absent,the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage.While for sufficient t,the antiferromagnetic spin correlation between dots is enhanced,and the conductance is strongly suppressed for the bonding state is almost doubly occupied.     

Thermal Entanglement and Correlated Coherence in Two Coupled Double Quantum Dots Systems

In this work, the thermal quantum correlations in two coupled double semiconductor charge qubits are investigated. This is carried out by deriving analytical expressions for both the thermal concurrence and the correlated coherence. The effects of the tunneling parameters, the Coulomb interaction, and the temperature on the thermal entanglement and on the correlated coherence are studied in detail. It is found that the Coulomb potential plays an important role in the thermal entanglement and in the correlated coherence of the system. The results also indicate that the Coulomb potential can be used for significant enhancement of the thermal entanglement and quantum coherence. One interesting aspect is that the correlated coherence capture all the thermal entanglement at low temperatures, that is, the local coherences are totally transferred to the thermal entanglement. Finally, the role played by thermal entanglement and the correlated coherence responsible for quantum correlations are focused on. It is shown that in all cases, the correlated coherence is more robust than the thermal entanglement so that quantum algorithms based only on correlated coherence may be more robust than those based on entanglement.     

The Spectra of Two-Electron Quantum Dot: Shifted 1/N Method

The spectra of two-electron quantum dot in a magnetic field of arbitrary strength is studied by using the shifted 1/N expansion method. The comparisons show that our results are in good agreement with the results of fixed-phase quantum Monte Carlo method and exact ones [Bolton, Phys. Rev. B54 (1996) 47801.     

基于投影纠缠对态算法优化的研究

二维强关联电子量子格点系统的投影纠缠对态(PEPS)算法是数值计算领域中研究二维强关联电子量子格点系统最为重要的张量网络算法.基于PEPS算法研究二维量子XYX模型与二维量子Ising模型,本文对PEPS算法进行了一些优化和改进研究,这些优化和改进主要体现在如何进行PEPS张量的更新与如何进行物理观测量的计算这两个方面,从而可以大大提高计算资源的利用.因而优化和改进后的PEPS算法可为研究热力学极限下的二维强关联电子量子格点系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

Quasi‐particle peak due to magnetic order in strongly correlated electron systems

We study the electron spectral function of the antiferromagnetically ordered phase of the three dimensional Hubbard model, using recently formulated low‐energy theory based on the 2D half‐filled Hubbard model which describes both collective spin and charge fluctuations for arbitrary value of the Coulomb repulsion U. The model then is solved by a saddle‐point approximation within the CP¹ representation for the Neel field. The single‐particle properties are obtained by writing the fermion field in terms of a U(1) phase, Schwinger boson SU(2) fields and a pseudofermion variables. We demonstrate that the appearance of a sharp peak in the electron spectral function in the antiferromagnetic state points to the emergence of the bosonic mode, which is associated with spin ordering.     

外电场下极性量子阱中杂质态结合能

我们用变分方法研究了外电场下量子阱中的杂质态结合能,计算中既考虑了电子同体纵光学声子和界面光学声子的相互作用又考虑了杂质中心同体纵光学声子和界面光学声子的相互作用。我们以GaAs/Al_0.3Ga_0.7As量子阱为例,讨论了结合能随杂质位置、阱宽和电场强度的变化规律。得到了电子-声子相互作用对杂质态结合能和斯塔克效应的修正是相当明显的。     

Electronic States of a Shallow Hydrogenic Donor Impurity in Different Shaped Semiconductor Quantum Wells

The shallow hydrogenic donor impurity states in square, V-shaped, and parabolic quantum wells are studied in the framework of effective-mass envelope-function theory using the plane wave basis. The first four impurity energy levels and binding energy of the ground state are more easily calculated than with the variation method. The calculation results indicate that impurity energy levels decrease withthe increase of the well width and decrease quickly when the well width is small.The binding energy of the ground state increases until it reaches a maximum value,and then decreases as the well width increases. The results are meaningful andcan be widely applied in the design of various optoelectronic devices.     

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. Néel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half J ₁–J ₂ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at J ₂/J ₁=0.5. The dimerized phase is stable over a range of values for J ₂/J ₁ around 0.5, and results for the ground-state energies are in good agreement with the results of exact diagonalizations of finite-length chains in this regime. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of J ₂/J ₁. A radical change is also observed in the behavior of the CCM sublattice magnetization as we enter the dimerized phase. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases. Once again, very good results for the ground-state energies are obtained. We find CCM critical points of the bra-state equations that are in agreement with the known phase transition point for this model. The results for the sublattice magnetization remain near to the “true” value of zero over much of the dimerized regime, although they diverge exactly at the critical point. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV₄O₉ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, Néel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits. Furthermore, we estimate the range over which the Néel order is stable, and we find the CCM result is in reasonable agreement with the results obtained by other methods. Our new approach has the dual advantages that it is simple to implement and that existing CCM codes for independent-spin product model states may be used from the outset. Furthermore, it also greatly extends the range of applicability to which the CCM may be applied. We believe that the CCM now provides an excellent choice of method for the study of systems with valence-bond quantum ground states.