Strong Coupling Expansions for Models of Strongly Correlated Electrons

强相关电子模型的强耦合展开式

• 批准号: 0105659
• 负责人: William Putikka
• 金额: $ 18万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-15 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0105659&HistoricalAwards=false
• 关键词: Strong; Coupling; Expansions; Models; Strongly

The properties of strongly correlated electrons in reduced dimensions remain some of the most fascinating problems in condensed matter physics. The discovery of high temperature superconductivity focused attention on two-dimensional models, with the copper oxide plane found in high temperature superconductors well described by a square lattice. The central theoretical hypothesis of research in high temperature superconductivity is that strong electronic correlations in reduced dimensions lead to enhanced superconducting correlations when the electrons are itinerant. A corollary of this hypothesis is that the low energy excitations in high temperature superconductors are anomalous due to strong correlations. Exactly how strong correlations produce these effects for two-dimensional systems, if at all, is currently not known.This research will study the effects of strong correlations and reduced dimensionality on systems of itinerant electrons by calculating high temperature series for correlation functions of the 2D t-J model. The 2D t-J model has been widely adopted as the fundamental model for high temperature superconductors. Direct numerical results are needed to sort through approximate analytic treatments of 2D strongly correlated electrons. High temperature series provide a means to obtain accurate, unbiased results in the thermodynamic limit for key properties of the 2D t-J model.The specific quantities to be calculated are thermodynamic properties, equal time correlation functions and zero frequency susceptibilities. The strength of superconducting correlations in the 2D t-J model are of key interest for applications to high temperature superconductivity. Series will be calculated for all possible symmetries of spin singlet pairing correlations. The full range of doping will be considered, from pseudogap behavior at small doping to the crossover to more conventional behavior at large doping. The zero frequency, wave vector dependent charge susceptibility will be used to search for charge stripe formation, while the zero frequency, wave vector dependent spin susceptibility will aid interpretation of NMR experiments. Equal time correlation functions and susceptibilities through their temperature derivatives can both be used to determine the momentum dependence of the low energy spin and charge excitations of the 2D t-J model. All quantities calculated for the full 2D square lattice will also be calculated for ladder lattices and other subsets of the square lattice with varying boundary conditions. This will allow a detailed study of boundary effects for systems of strongly correlated electrons. The series results will also be compared to density matrix renormalization group calculations on the same lattices and with the same boundary conditions.%%%Theoretical computational research will be conducted on a model for the behavior of electrons in the high temperature superconductors. The results will aid in understanding these intriguing, fundamental and potentially useful materials.***

在缩小的尺寸中，密切相关的电子的性质仍然是凝结物理学中最引人入胜的问题。 高温超导的发现将注意力集中在二维模型上，在高温超导体中发现了氧化铜平面，正方形晶格很好地描述了。 高温超导性研究的中心理论假设是，降低尺寸的强电子相关性会导致电子相关时增强的超导相关性。 该假设的必然性是高温超导体中的低能量激发由于相关性很强而异常。 确切的相关性如何为二维系统产生这些影响（如果有的话），目前尚不清楚。这项研究将通过计算2D T-J模型的相关功能来研究强相关性和降低尺寸对巡回电子系统的影响。 2D T-J模型已被广泛用作高温超导体的基本模型。 需要直接的数值结果来通过对2D强相关电子的近似分析处理进行分类。 高温序列提供了一种在2D T-J模型的关键特性的热力学限制中获得准确，无偏见的手段。要计算的特定数量是热力学特性，相等的时间相关函数和零频率敏感性。 2D T-J模型中超导相关性的强度对于高温超导性的应用引起了关键。 将针对自旋单重配对相关性的所有可能对称性计算系列。 将考虑各种兴奋剂，从小兴奋剂到跨界的伪行为到大掺杂时更常规的行为。 零频率，波矢量依赖电荷敏感性将用于搜索电荷条带的形成，而零频率，波矢量依赖性自旋敏感性将有助于解释NMR实验。 通过其温度导数的相关时间相关函数和敏感性都可以用于确定2D T-J模型的低能旋转和电荷激发的动量依赖性。还将计算出针对整个2D平方晶格计算的所有数量，还将计算出具有不同边界条件的正方形晶格的梯子和其他子集。 这将允许对强相关电子系统的边界效应进行详细研究。 该系列结果还将与在相同晶格上的密度矩阵重新归一化组计算进行比较。%% %%理论计算研究将对高温超导体中电子的行为进行模型进行。 结果将有助于理解这些有趣，基本和潜在有用的材料。***