若干一维自旋链中量子关联的研究

发布时间：2018-06-11 10:34

本文选题：临界自旋系统 + 三自旋相互作用　；参考：《南京师范大学》2016年博士论文

【摘要】：量子相变一直是凝聚态物理中的一个很重要的研究课题。传统上,量子相变一般在Ginzburg-Landau理论框架下用序参量和对称破缺机制来描述。最近,随着量子信息学的迅猛发展,从量子信息学的角度来研究量子相变问题得到了广泛的关注。本论文主要研究了量子失协,量子纠缠,量子相干和量子不确定度等量子信息概念与几个典型一维量子自旋模型的量子相变的关系。本论文的最后一部分,还研究了量子不确定度的动力学问题。首先,我们研究了一维横场中各向异性XY模型中最近邻格点的基态量子失协的尺寸效应,发现对于Ising相变,量子失协一阶导数的临界行为随各向异性参数的变化而不同；对于各向异性相变,在任意外场下,量子失协的导数在临界点随系统的尺寸都是对数发散的,这与模型中量子纠缠的表现不同。其次,我们研究了具有XZY-YZX型三自旋相互作用的一维横场各向异性XY模型中近邻格点间的基态量子失协。与一维横场各向异性XY模型相比较,除了有能隙的铁磁和顺磁相以外,具有三自旋相互作用的模型中还有一个无能隙的螺旋相。量子失协的一阶导数在有能隙的铁磁和顺磁相之间转变的临界点附近随系统的尺寸对数发散；在有能隙的铁磁或者铁磁相与无能隙的螺旋相之间转变的临界点附近,量子失协的一阶导数不随系统的大小变化。具有三自旋相互作用的一维横场各向同性XY模型具有两个无能隙的螺旋相,量子失协的导数在这两个无能隙的螺旋相之间转变的临界行为与其在有、无能隙的量子相之间转变的临界行为相似。然后,基于Wigner-Yanase反信息(Wigner-Yanase skew information)这一量,我们研究了一维横场中各向异性XY模型中的基态量子相干。发现对于Ising相变,量子相干的一阶导数在临界点附近都随系统的尺寸对数发散；对于各向异性相变,单自旋量子相干和双自旋局域σz量子相干恰在临界点处取得极值：而双自旋局域σx和σy量子相干在临界点附近的一阶导数随系统的尺寸线性对数发散,并具有完全相反的斜率和截距。对于具有三自旋相互作用的横场XY自旋链,有能隙的铁磁或顺磁相与无能隙的螺旋相转变的临界点附近,量子相干的导数不存在有限尺寸标度律。我们还研究了简化定义的量子相干,发现它的行为与其原始对应具有相似的特征。最后,我们研究了在阶梯跳变外场情况下一维横场XY自旋链的最近邻两自旋量子不确定度的时间动力学,讨论了温度的变化对量子不确定度的时间演化的影响。发现和量子纠缠相似,量子不确定度也存在时间演化的非遍历性。这种非遍历性,来自于系统本身的磁化强度和自旋关联函数的非遍历性。
[Abstract]:Quantum phase transition has been an important research topic in condensed matter physics. Traditionally, quantum phase transitions are generally described by order parameters and symmetric breaking mechanisms within the Ginzburg-Landau theory. Recently, with the rapid development of quantum informatics, the study of quantum phase transition from the perspective of quantum informatics has received extensive attention. In this paper, the relationship between quantum information concepts, such as quantum disconnection, quantum entanglement, quantum coherence and quantum uncertainty, and quantum phase transitions of several typical one-dimensional quantum spin models is studied. In the last part of this thesis, we also study the dynamics of quantum uncertainty. First, we study the size effect of ground state quantum disconnection in anisotropic XY model in one-dimensional transverse field. It is found that for Ising phase transition, the critical behavior of the first derivative is different with the variation of anisotropic parameters. For anisotropic phase transitions, the derivative of quantum disconnection is logarithmic at the critical point at any external field, which is different from the quantum entanglement in the model. Secondly, we study the ground state quantum disconnection between nearest neighbor lattice points in one dimensional transverse anisotropic XY model with XZY-YZX type three-spin interaction. Compared with the one-dimensional anisotropic XY model of transverse field, there is a helical phase without energy gap in the model with three spins in addition to the ferromagnetic and paramagnetic phase with energy gap. The first derivative of quantum disconnection diverges with the logarithm of the system size near the critical point of transition between ferromagnetic and paramagnetic phase with energy gap, and near the critical point of transition between ferromagnetic or ferromagnetic phase with energy gap and helical phase without energy gap. The first derivative of quantum disconnection does not vary with the size of the system. The one-dimensional transversely isotropic XY model with three-spin interaction has two helical phases with no energy gap. The critical behavior of transition between quantum phases without energy gap is similar. Then, based on the Wigner-Yanase inverse information (Wigner-Yanase skew information), we study ground state quantum coherence in an anisotropic XY model in one dimensional transverse field. It is found that for the Ising phase transition, the first derivative of quantum coherence diverges with the logarithm of the system size near the critical point, and for the anisotropic phase transition, The single spin quantum coherence and the double spin local 蟽 z quantum coherence obtain the extremum at the critical point. The first derivative of the double spin local 蟽 x and 蟽 y quantum coherence diverges linearly with the size of the system, and the first derivative of the double spin local 蟽 x and 蟽 y quantum coherence diverges linearly with the size of the system. And has completely opposite slope and intercept. For a transverse field XY spin chain with three spins, the derivative of quantum coherence does not have a finite scale law near the critical point of transition between ferromagnetic or paramagnetic phase with band gap and helical phase without energy gap. We also study the simplified definition of quantum coherence and find that its behavior is similar to its original counterpart. Finally, we study the time dynamics of the nearest neighbor two spin quantum uncertainty of one dimensional transverse field XY spin chain in the case of step jump field, and discuss the influence of temperature change on the time evolution of quantum uncertainty. Similar to quantum entanglement, quantum uncertainty has non-ergodicity of time evolution. This non-ergodicity comes from the magnetization of the system itself and the non-ergodicity of the spin correlation function.
【学位授予单位】：南京师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413;O469

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