Self-consistent treatment of disorder-induced interacting criticality

疾病引起的相互作用临界性的自洽治疗

• 批准号: 430195475
• 负责人: Professor Dr. Ferdinand Evers
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/430195475?language=en
• 关键词: Self; consistent; treatment; disorder; induced

The project goal is to achieve an improved understanding of self-consistent field (scf) theories of disorder-induced interacting criticality. The corresponding ensembles of scf-random Hamiltonians can be categorised acording to the Altland-Zirnbauer symmetry classification.Remarkably, the scf-condition can induce extra correlations among single-particle states of the scf-Hamiltonian that can result in new phase diagram. Physically, scf-ensembles are important because they provide the reference point for a perturbative analysis of interaction effects in disordered fermion systems. Also they are important because understanding the mean-field behavior is a prerequisite for revealing the effect of interaction-mediated quantum fluctuations. Finally, scf-random Hamiltonians provide a rich and largely unexplored field for fundamental research in mathematical physics.The focus of this project is on the Hartree-Fock theory and the Boguluibov-deGennes theory of disordered electrons in the presence of repulsive or pairing interactions. We will solve the corresponding problems by combined numerical and theoretical efforts. On the one hand, we will implement and improve numerical codes for these problems employing the kernel-polynomial-method. Thus, extensive numerical data can be generated for spin-full and spin-less models of very large system sizes. On the other hand, we will develop the analytical theory (of the nonlinear sigma model type) for scf-Hamiltonians in the weak disorder regime. In a concerted effort the simulation data will be contrasted against and analysed with the help of the theoretical results. Both approaches, numerics and field theory, complement each other ideally. Numerics allows to treat even strong-disorder effects exactly, but can only generate a limited understanding per se, because for this analytical formulae are required. Such formulae can be generated, e.g., with field-theoretic approaches; hower, with good control this can be achieved only in a relatively small sector parameter space. By combining both approaches, and only by combining, a deeper understanding of the physics in the full parameter space can be achieved. Both project teams have already successfully collaborated in this way before and the experiences made in this way are very encouraging.

该项目的目标是实现一个更好的理解自洽场（scf）理论的无序诱导相互作用的临界性。相应的自洽场随机哈密顿量系综可以根据Altland-Zirnbauer对称性分类进行分类，值得注意的是，自洽场条件可以在自洽场随机哈密顿量的单粒子态之间引入额外的关联，从而产生新的相图. 在物理上，自洽场系综是很重要的，因为它们为无序费米子系统中相互作用效应的微扰分析提供了参考点。它们也很重要，因为理解平均场行为是揭示相互作用介导的量子涨落效应的先决条件。最后，SCF-随机哈密顿量为数学物理的基础研究提供了一个丰富的和基本上未开发的领域。本项目的重点是Hartree-Fock理论和Boguluibov-deGennes理论中存在的排斥或配对相互作用的无序电子。我们将结合数值和理论的努力解决相应的问题。一方面，我们将采用核多项式方法实现和改进这些问题的数值代码。因此，广泛的数值数据可以产生非常大的系统尺寸的自旋完整和自旋少的模型。 另一方面，我们将发展的分析理论（非线性西格玛模型类型）的SCF-哈密顿在弱无序制度。在协调一致的努力中，模拟数据将与理论结果进行对比和分析。这两种方法，数值和场论，相互补充理想。数值可以精确地处理甚至强无序效应，但只能产生有限的理解本身，因为这需要分析公式。可以生成这样的公式，例如，利用场论方法;然而，利用良好的控制，这只能在相对小的扇区参数空间中实现。通过结合这两种方法，并且只有通过结合，才能更深入地理解全参数空间中的物理学。 这两个项目小组以前已经成功地以这种方式合作，这种方式取得的经验非常令人鼓舞。