低維強(qiáng)關(guān)聯(lián)系統(tǒng)的量子相變與量子糾纏.pdf

1、There have been much interest in the study of spin models with orbital degeneracy[l, 2, 3, 4, 5, 6, 7, 8, 9, 10] due to experimental progress related to many transition-metal and rare-earth compounds such as LaMnO<,3>，C

2、eB<,6>, and perovskite lattice,as in KCuF<,3>[6, 5]. Those systems involve orbital degree of freedom in addition tospin ones. Almost three decades ago, Kugel and Khomskii[ll] had pointed out thepossibility of orbital exc

3、itations in these systems. As a model system, it exhibitssome fascinating physical features which is lack without orbital degree of freedomThe isotropic case of spin system with orbital degeneracy was shown to have an en

4、-larged SU(4) symmetry [1], and one dimensional model is known to exactly solvable[2, 12」. Materials related to spin-orbital systems in one dimension include quasi-one-dimensional tetrahis-dimethylamino-ethylene (TDAE)-C

5、<,60>[13], artificial quan-tum dot arrays[14], and degenerate chains in Na<,2>Ti<,2>Sb<,2>O and Na<,2>V<,2>O<,5> compounds[15, 16]. It is therefore worthwhile to systematically study the features of one di-mensional mode

6、l. Theoretical studies[2] has found the strong interplay of orbitaland spin degrees of freedom in the excitations spectra. It has been noticed that;the presence of orbital may results in various interesting magnetic prop

7、erties. Ap-plying a conventional magnetic field, the spin orbital chain with SU(4) symmetryis shown to reduce to a model with orbital SU(2) symmetry[9] in the ground state.Recent壇we showed that the magnetization process

8、becomes more complicated iftaking account of the contribution from orbital sector [10]. We have explained thatthe competition between spin and orbital degree of freedom leads to an orbital anti-polarization phase. Howeve

9、r, the external field we introduced in ref[10」 is not themost general one for SU(4) systems. Both the anisotropy in spin-orbital superex-change and John-Teller distortion which breaks the degeneracy of。，orbital [5[, this

10、allows us to consider the most generalized external fields in the spin-orbital systems. Thus the first focus of this report is to study a SU(4) spin-orbital chain in thepresence of a generalized external field on the

11、basis of its Bethe ansatz solution. Byintroducing three Lande g factors for spin, orbital and their products in the SU(4)Zeeman term, we will discuss systematically the various symmetry breaking inducedby a generalized f

12、ield. The magnetization versus the external field are obtained bysolving Bethe-ansatz equations numerically.Quantum entanglement, as one of the most intriguing feature of quantum the-ory, has been a subject of much stud

13、y recent years, mostly because its nonlocalconnotation[17] is regarded as a valuable resource in quantum communication andinformation processing[18, 19]. For example,an entangled state, such as a singletstate1/2<'1/2>一[

14、jj)), can be used for the realization of teleportationC201. On theoiner nana, as wren otner resources, such as tree enerLv and information. one wouldlike to know how it can be quantified and controlled. For the first pro

15、blem, muchefforts have been devoted to develop a quantitative theory of entanglement, include:entanglement of formation[21, 22, 23, 24], which is regarded as its basic measure.For the second problem, many authors[25, 26,

16、 27, 28, 29, 30, 31, 32, 33] tried tobuilt bridge between quantum entanglement and physical models by investigatingtheir entanglement in both the ground state[25, 321 and thermal state[30, 31] Very recent玩the intriguin

17、g issue of the, relation between entanglement andquantum phase transition have been addressed[33, 341. For a spin-1/2 ferromagneticchain, Osterloh et. al.，reported that the entanglement shows scaling behavior in thevicin

18、ity of quantum phase transition point (351 as induced勿a transverse magneticfield. Vidal et. al. tried to establish a connection between quantum informationand condensed matter theory by studying the behavior of critical

19、entanglement inspin systems. So it is believed that the entanglement of the .ground state; likethe conductivity in the Mott-insulator transition[361 and quantum Hall effect, andmagnetization in the external-field-induced

20、 phase transition, is also plays a crucialrole to the understanding of quantum phase transition. On the other hand, grouptheory as well as symmetry of the system are parts of the foundation of quantummechanics[37, 381, t

21、he knowledge of its presence often makes it easy to understandthe physics. Thus the study of entanglement at the ground state and its relation tothe group theory will not only have a contribution to experimental realizat

22、ion, butalso enriches our physical intuition of quantum theoryThe second focus of the report is to study the properties of ground state con-currence of an antiferromagnetic XXZ chain.- We will show that the competitionb

23、etween quantum fluctuation and ordering will lead to maximum value of concur-rence at the isotropic point. This observation could also be clarified from the point.view of q-deformation theory. The concurrence's dependenc

24、e on anisotropic parame-ter△is presented both numerically and analytically. The relation of the concurrenceto the correlation length } in the Ising-like insulating phase, as well as the scalingbehavior around the critica

25、l point△=1 where the Metal-insulator quantum phasetransition occurs, are also discussed. Thus our result not only manifest interestingphysical phenomenon, but also establish non-trivial connection between the quanti-ties