新千年理论物理的走向——参加新加坡国际数学、理论物理大会有感

新千年始,基础科学国际大会“数学和理论物理在21世纪的挑战”于2000年3月13—17日在新加坡举行.1　大会要点综述11　大会宗旨人类进入新千年,对基础科学:数学和理论物理的进展和取得的成就进行回顾,以激励后人不断奋进,取得更大的辉煌.随着商品经济的迅猛发展,基础科研人员及其后备力量———求学于数学和理论物理的学生,大量流失于面向市场经济效益的高科技领域、ＩＴ业、金融业、生物工程业等,极大地影响了青年学子的择业观.作为高科技发展后劲基石的数学和理论物理何去何从,成为各国政府制定科技政策时深入研讨的重点.在世纪之交,科教兴…     

Light-Induced Hofstadter＇s Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagomé Lattice

We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper＇s equations from the Schr？dinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper＇s equations. We analyze the properties of the Hofstadter＇s butterfly spectrum and discuss its observability.     

Scaling of entanglement entropy for spin chain with Dzyaloshinskii-Moriya interaction

This paper investigates the entanglement in an XX-type spin chain with Dzyaloshinskii-Moriya interaction under an external magnetic field.The von Neumann entropy of entanglement between two blocks for the ground state of the system is evaluated.It analyses and discusses the scaling behaviour of the entanglement entropy.     

Reduced Properties and Applications of Y（sl（2）） Algebra for a Two-Spin System

By taking a special constraint for a general realization of Y（sl（2））, two sets of sl（2） algebras are presented, in which a u（1） algebra is hidden. With the help of this constraint, the block-diagonal form can be written to the generator J of Yangian algebras, and especially it is a rotational transformation of a spin in the elementary quantum mechanics. This sheds new light on the physical meaning of Y （sl（2） ）.     

Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling

We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling. We calculate the band structure of the lattice and evaluate the Z2 topological indices. According to the Z2 topological indices and the band structure, we present the phase diagrams of the lattice with different filling fractions. We find that topological insulators occur in some range of parameters at 1/6, 1/3, 1/2, 2/3 and 5/6 filling fractions. We analyze and discuss the characteristics of these topological insulators and their edge states.     

Hofstadter＇s Butterfly and Phase Transition of Checkerboard Superconducting Network in a Magnetic Field

We study the magnetic effect of the checkerboard superconducting wire network. Based on the de Gennes- Alexader theory, we obtain difference equations for superconducting order parameter in the wire network. Through solving these difference equations, we obtain the eigenvalues, linked to the coherence length, as a function of magnetic field. The diagram of eigenvalues shows a fractal structure, being so-called Hofstadter＇s butterfly. We also calculate and discuss the dependence of the transition temperature of the checkerboard superconducting wire network on the applied magnetic field, which is related to up-edge of the Hofstadter＇s butterfly spectrum.     

Two-Qubit Quantum Logic Gate in Molecular Magnets

We propose a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled singlemolecule magnets, [Mn4]2. We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between a pair of the four quantum computing bases and between the quantum computing bases and excited states are evaluated and analysed.     

Topological Insulators in α-Graphyne

In this paper, we investigate topological phases of α-graphyne with tight-binding method. By calculating the topological invariant Z2 and the edge states, we identify topological insulators. We present the phase diagrams of α-graphyne with different filling fractions as a function of spin-orbit interaction and the nearest-neighbor hopping energy. We find there exist topological insulators in α-graphyne. We analyze and discuss the characteristics of topological phases of α-graphyne.     

Thermal entanglement in molecular spin rings

The thermal entanglement in the triangular molecular spin ring with Dzyaloshinskii-Moriya interaction is studied.The concurrences of arbitrary two spins of the triangular molecular spin ring for various cases are evaluated.The tendency of the concurrence with Dzyaloshinskii-Moriya interaction and temperature is analysed and discussed.We note that the concurrence arrives at its maximum in the regime with the large Dzyaloshinskii-Moriya interaction and low temperature,and gradually decreases to zero with the increase of temperature.The concurrence has different features for the ferromagnetic and antiferromagnetic cases.For completeness,we also numerically calculate the concurrence of spin rings with N > 3 spins and analyse their behaviours.