The dynamics of quantum discord and entanglement of two atoms coupled to two spatially separate cavities in cavity QED

We demonstrate that a kind of highly excited state of strongly attractive Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in the spin-1/2 Fermi optical lattice system by a sudden switch of interaction from the strongly repulsive regime to the strongly attractive regime. In contrast to the ground state of the attractive Hubbard model, such a state is the lowest scattering state with no pairing between attractive fermions. With the aid of Bethe-ansatz method, we calculate energies of both the Fermi Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2 ultracold fermions and show that both energies approach to the same limit as the strength of the interaction goes to infinity. By exactly solving the quench dynamics of the Hubbard model, we demonstrate that the Fermi super-Tonks-Girardeau state can be transferred from the initial repulsive ground state very efficiently. This allows the experimental study of properties of Fermi super-Tonks-Girardeau gas in optical lattices.     

Persistent currents in a lattice correlated electron ring with a magnetic impurity

The behavior of charge and spin persistent currents in an integrable lattice ring of strongly correlated electrons with a magnetic impurity is exactly studied. Our results manifest that the oscillations of charge and spin persistent currents are similar to the ones, earlier obtained for integrable continuum models with a magnetic impurity. The difference is due to two (instead of one) Fermi velocities of low-lying excitations. The form of oscillations in the ground state is “saw-tooth”-like, generic for any multi-particle coherent one-dimensional models. The integrable magnetic impurity introduces net charge and spin chiralities in the generic integrable lattice system, which determine the initial phase shifts of charge and spin persistent currents. We show that the magnitude of the charge persistent current in the generic Kondo situation does not depend on the parameters of the magnetic impurity, unlike the (magneto)resistivity of transport currents. Received 30 January 2003 / Received in final form 12 March 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: zvyagin@fy.chalmers.se     

Variational approach to spin fluctuations in the Hubbard model

We study a one parameter variational wave function to improve the spin density wave ground state of the Hubbard model by inclusion of quantum spin fluctuations. Using a perturbative approach and novel lattice summation techniques we present analytical as well as numerical results for the correlation energies and the staggered magnetizations in one and two dimensions. We find ground state energies which are satisfyingly close to known exact results and are significantly lower than those of existing Gutzwiller and numerical treatments.     

Spin-charge density waves in the Hubbard model

The ground state of the Hubbard model in a square lattice is examined in the Hartree-Fock mean field approximation at zero temperature. At small finite hole doping, the system has periodically distributed soliton like structures whose modulations are incommensurate. In a self-consistent way, the Fermi energy can always be located in a gap. The incommensurate states have lower energies than the commensurate antiferromagnetic states calculated at the same filling. These soliton structures persist even when a sizeable nearest neighbor repulsive interaction is included.     

玻色爱因斯坦凝聚体中杂质的相互作用

文章研究了两个杂质浸入玻色凝聚体中的相互作用.通过使用微扰法,计算了在弱杂质-玻色子相互作用区域中的基态能量.结果表明基态能量与两杂质之间的相对距离有关.从基态能量出发,研究发现不管杂质与玻色子相互作用是处在排斥状态还是吸引状态,两杂质之间都有保持吸引趋势;而当一个杂质与玻色子相互作用是吸引时,另一个为排斥时,两个杂质之间呈现出了排斥的效果.通过杂质之间有效力的计算也验证了上述现象,进一步研究凝聚体密度背后的力学机制,再次得出了一致结论.     

Exact solution of an impurity semiconductor model by Hamiltonian renormalization

In this paper, we present exact solutions for a semiconductor model treated in the framework of Wegner's flow equation (continuous Hamiltonian renormalization) method. We considered as model a two-band Anderson impurity Hamiltonian with band–band and band–impurity hybridization and also with e–e interaction on the localized states of the impurity. Exact solutions are obtained for the renormalized level of the impurity for both vanishing and non-vanishing Hubbard term. The bands–impurity hybridization couplings vanish as a result of the flow-renormalization while the band energies do not change (as required).     

Phase behaviors of strongly correlated Fermi gases in one-dimensional confinements

We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k _F → 4k _F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.     

Topological Hubbard model and its high-temperature quantum Hall effect

The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is sufficiently strong. We ponder on the possible practical applications, beyond metrology, that the quantized charge Hall effect might have if it could be realized at high temperatures and without external magnetic fields in strongly correlated materials.     

Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

We study the delocalization effect of a short-range repulsive interaction on the ground state of a finite density of spinless fermions in strongly disordered one dimensional lattices. The density matrix renormalization group method is used to explore the charge density and the sensitivity of the ground state energy with respect to the boundary condition (the persistent current) for a wide range of parameters (carrier density, interaction and disorder). Analytical approaches are developed and allow to understand some mechanisms and limiting conditions. For weak interaction strength, one has a Fermi glass of Anderson localized states, while in the opposite limit of strong interaction, one has a correlated array of charges (Mott insulator). In the two cases, the system is strongly insulating and the ground state energy is essentially invariant under a twist of the boundary conditions. Reducing the interaction strength from large to intermediate values, the quantum melting of the solid array gives rise to a more homogeneous distribution of charges, and the ground state energy changes when the boundary conditions are twisted. In individual chains, this melting occurs by abrupt steps located at sample-dependent values of the interaction where an (avoided) level crossing between the ground state and the first excitation can be observed. Important charge reorganizations take place at the avoided crossings and the persistent currents are strongly enhanced around the corresponding interaction value. These large delocalization effects become smeared and reduced after ensemble averaging. They mainly characterize half filling and strong disorder, but they persist away of this optimal condition. Received 5 July 2000 and Received in final form 8 November 2000     

Cold attractive spin polarized Fermi lattice gases and the doped positive U Hubbard model

Experiments on polarized fermion gases performed by trapping ultracold atoms in optical lattices allow the study of an attractive Hubbard model for which the strength of the on-site interaction is tuned by means of a Feshbach resonance. Using a well-known particle-hole transformation we discuss how results obtained for this system can be reinterpreted in the context of a doped repulsive Hubbard model. In particular, we show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state corresponds to the striped state of the two-dimensional doped positive U Hubbard model. We then use the results of numerical studies of the striped state to relate the periodicity of the FFLO state to the spin polarization. We also comment on the relationship of the d(x(2)-y(2)) superconducting phase of the doped 2D repulsive Hubbard model to a d-wave spin density wave state for the attractive case.     

Emergence of non-equilibrium superconductivity originated from repulsive interaction: Demonstration using optical lattices and implication to solid-state matter system

We study the dynamical properties of ultracold fermions in one-dimensional optical superlattices by using the adaptive time-dependent density matrix renormalization group method. The system is repulsive Hubbard model with an two-site periodic superlattice potential. Owing to superlattice structure, the ground-state states become the Mott-type insulating state at quarter-filling and band-type insulating state at half-filling, respectively. We clarify the dynamical properties of time evolution when the system is non-adiabatically changed to another lattice structure (i.e., the superlattice potential is suddenly changed to a normal one). In the case of Mott-type insulating state at quarter-filling, the time evolution exhibits a profile similar to that expected for single atom. On the other hand, we clarify the dynamical properties of a band-type insulating state at half-filling. The strongly-correlated interaction an unusual pairing of fermions induced the pair hopping process. We further address the robustness of pair hopping process and possibility of superconductivity by using sudden change from superlattice structure to normal one.     

Charge Gap in One-Dimensional Extended Hubbard Model

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.     

Variational pair theory of the attractive and extended Hubbard model ind-dimensions

We present a variational approach for treating the Hubbard Hamiltonian in one, two and three dimensions. It is based on 2M-fermion wavefunctions which are allowed to form correlated spin-singlet pairs. Expressions for the ground state energy and correlation functions are derived in terms of general pair coefficient functions. The presented approach offers a convenient starting point for improved variational treatments that allow to include different specific types of pair correlations. We present first applications to the attractive and to the extended Hubbard model using a very simple ansatz for the pair coefficient functions. The ground state energy, chemical potential, order parameter, momentum distribution as well as spin-spin and density-density correlation functions follow from a system of coupled nonlinear equations that has to be solved selfconsistently. All quantities are given for arbitrary band-filling in one, two and three dimensions. Our results are compared with those of other approximations and for the one-dimensional case with the exact results of Krivnov and Ovchinnikov.     

The embedding method beyond the single-channel case

We investigate the relationship between persistent currents in multi-channel rings containing an embedded scatterer and the conductance through the same scatterer attached to leads. The case of two uncoupled channels corresponds to a Hubbard chain, for which the one-dimensional embedding method is readily generalized. Various tests are carried out to validate this new procedure, and the conductance of short one-dimensional Hubbard chains attached to perfect leads is computed for different system sizes and interaction strengths. In the case of two coupled channels the conductance can be obtained from a statistical analysis of the persistent current or by reducing the multi-channel scattering problem to several single-channel setups.     

硅纳米结构晶体管中与杂质量子点相关的量子输运

在小于10 nm的沟道空间中,杂质数目和杂质波动范围变得十分有限,这对器件性能有很大的影响.局域纳米空间中的电离杂质还能够展现出量子点特性,为电荷输运提供两个分立的杂质能级.利用杂质原子作为量子输运构件的硅纳米结构晶体管有望成为未来量子计算电路的基本组成器件.本文结合安德森定域化理论和Hubbard带模型对单个、分立和耦合杂质原子系统中的量子输运特性进行了综述,系统介绍了提升杂质原子晶体管工作温度的方法.     

Validation of the Ability of Full Configuration Interaction Quantum Monte Carlo for Studying the 2D Hubbard Model

To validate the ability of full configuration interaction quantum Monte Carlo(FCIQMC) for studying the 2 D Hubbard model near half-filling regime, the ground state energies of a 4 x 4 square lattice system with various interaction strengths are calculated. It is found that the calculated results are in good agreement with those obtained by exact diagonalization(i.e., the exact values for a given basis set) when the population of psi particles(psips) is higher than the critical population required to correctly sample the ground state wave function. In addition, the variations of the average computational time per 20 Monte Carlo cycles with the coupling strength and the number of processors are also analyzed. The calculated results show that the computational efficiency of an FCIQMC calculation is mainly affected by the total population of psips and the communication between processors. These results can provide useful references for understanding the FCIQMC algorithm, studying the ground state properties of the 2 D Hubbard model for the larger system size by the FCIQMC method and using a computational budget as effectively as possible.     

CHARGE AND SPIN GAPS IN THE DIMERIZED HUBBARD MODEL

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in the one-dimensional dimerized Hubbard model. The formation of charge and spin gaps is investigated both for the half-filled electron band and away from the half-filled band. The scaling laws of the charge and spin gaps with the dimerization parameterΔ and the repulsive interaction strength U are obtained.     

Correlations in the ground state of the one-dimensional Hubbard model

With eigenfunctional theory and a rigorous expression of exchange-correlation energy of a general interacting electron system, we study the ground state properties of the one-dimensional Hubbard model, and calculate the ground-state energy as well as the charge gap at half-filling for arbitrary coupling strength u=U/(4t) and electron density nc. We find that the simple linear approximation of the phase field works well in weak coupling case, but it becomes inappropriate as the on-site Coulomb interaction becomes strong where the fluctuations of the bosonic auxiliary field are strong. Then we propose a new scheme by adding Gutzwiller projection which suppresses the density fluctuations and the new results are quite close to the exact ones up to considerably strong coupling strength u=3.0 and for arbitrary electron density nc. Our calculation scheme is proved to be effective for strongly correlated electron systems in one dimension, and its extension to higher dimensions is straightforward.