Theory of properties of some one-dimensional systems
Theory of properties of some one-dimensional systems
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发表时间：
1977
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通讯作者：
L. Gonçalves
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作者：
L. Gonçalves
本文主要是对一些一维模型进行理论研究。特别注意简单但不平凡的可溶模型。本研究首先对格林函数方法进行了概述，这是贯穿本研究的形式主义。讨论了电子-声子和自旋声子耦合系统，并介绍了一种解耦方案。该近似准确地给出了一维系统的转变温度，即T = 0，因此在平均场近似上有了很大的改进。研究了横向场中的不纯xy链，给出了其形式解。讨论了静态相关性和时变相关性，并详细讨论了边界项的影响。求解了各向同性链的单杂质情况，并给出了如何由此推导出开链结果的热力学极限。通过求解能量密度连续方程，得到了非纯各向同性链的热流算符。在几种近似中讨论了一维横向Ising模型的动力学。详细检查了每种近似的局限性，并使用最成功的近似计算了随时间变化的相关性。还表明，这种近似只在高温极限下有效，在这种情况下没有观察到临界行为。在两种不同的情况下，将各向同性不纯xy链的单杂质溶液推广到许多杂质。在第一种情况下，在平均t矩阵近似的框架下计算了稀链的比热，并将结果与有限链的精确数值计算进行了比较。在第二种情况下，各向同性xy链在随机横向场中的比热和导热系数使用相干势近似（CPA）计算。所得结果可用于解释硫酸乙基镨的低温热性能。最后，在简要讨论了所谓的佩尔斯不稳定性之后，研究了两个相互作用系统，一个电子-声子系统和一个自旋声子系统。第一个模型是在工作开始时讨论的近似框架内精确求解的。它呈现出一个巨大的科恩异常在零度驱动佩尔斯转变。讨论了重正一化模式，给出了波矢量π / a、若干耦合常数和温度下声子传播体的实部和虚部。自旋声子系统也在本文最初讨论的近似框架中进行了研究，并且选择了这样一种方式，即根据横向Ising模型中计算的格林函数给出相关性质。本文采用了该模型的动力学结果，由于这些结果仅在高温极限下有效，因此讨论仅限于该温度区域。由于该区域远离临界区域，因此没有观察到临界行为，研究仅限于简单的模态讨论。给出了在波矢量π / a、高温和各种耦合常数条件下重整化声子传播体的实部和虚部。
This thesis consists in a theoretical study of some one-dimensional models. Special attention is given to simple but non-trivial soluble models. The study starts with a resume of the Green function method which is the formalism used throughout the work. A discussion of coupled electron-phonon and spin-phonon systems is presented and a decoupling scheme introduced. The approximation gives the transition temperature for one-dimensional systems exactly, namely T = 0, and consequently represents a great improvement on the mean-field approximation. The impure XY-chain in a transverse field is studied and the formal solution presented. The static and time-dependent correlations are discussed, and the effect of the boundary term reviewed in details. The one-impurity case is solved for the isotropic chain, and it is shown how to derive from it the open chain result in the thermodynamic limit. The heat-flux operator is obtained for the impure isotropic chain by solving the continuity equation for energy density. The dynamics of the one-dimensional transverse Ising model is discussed within several approximations. The limitations of each approximation are examined in detail and the time-dependent correlations are calculated using the most successful approximation. It is also shown that this approximation is only valid in the high temperature limit in which case no critical behaviour is to be observed. The one-impurity solution of the isotropic impure XY-chain is extended to many impurities in two different cases. In the first case the specific heat of the dilute chain is calculated in the framework of the average t-matrix approximation, and the results compared with exact numerical calculations for finite chains. In the second case the specific heat and thermal conductivity of the isotropic XY-chain in a random transverse field are calculated using the coherent-potential approximation (CPA). The results are used to explain the low temperature thermal properties of praseodymium ethyl sulphate. Finally, two interacting systems, an electron-phonon system and a spin-phonon system, are studied after a brief discussion of the so-called Peierls instability. The first model is solved exactly in the framework of the approximation discussed at the beginning of the work. It presents a giant Kohn anomaly at zero temperature which drives a Peierls transition. The renormalized modes are discussed, and the real and imaginary parts of the phonon propagator are presented for wave vector π ⁄ a and several coupling constants and temperatures. The spin-phonon system is also studied in the framework of the approximation discussed initially in the work, and it is chosen in such a way that the relevant properties are given in terms of Green functions calculated in the transverse Ising model. The results obtained for the dynamics of this model are used, and since they are valid only in the high temperature limit, the discussion is restricted to this temperature region. Since this region is far away from the critical one, no critical behaviour is observed, and the study is restricted to a simple discussion of modes. The real and imaginary parts of the renormalized phonon propagator are presented for the wave vector π ⁄ a , high temperature and various coupling constants.