Density Matrix Renormalization Group Studies of Strongly Correlated Systems

这笔赠款支持了对低维强相互作用电子系统性质的理论研究。特别是，这项研究将进一步发展与密度矩阵重整化群方法相关的算法，使这种计算方法可以应用于更广泛的凝聚态系统和现象。凝聚态物理中最令人兴奋的领域之一是研究低维系统中的强关联效应。这些体系表现出广泛的行为，如高温超导、反铁磁性、条状和自旋液体相。随着制造技术发展对纳米尺度的控制，它们也显示出巨大的前景，用于新一代电子和自旋电子器件。为了理解这些系统，数值模拟技术变得越来越必要，因为这些系统具有强耦合项和不同类型阶次之间的竞争。主要研究者(PI)是密度矩阵重整化群(DMRG)的创建者，密度矩阵重整化群是研究强关联系统最有效的数值方法之一。Pi和他的团队将DMRG应用于各种这样的系统，包括自旋链、梯子、Y结，包括纯自旋系统和空穴掺杂系统。了解这些系统的动力学性质对于与实验进行比较和描述输运是必不可少的。最近，在DMRG内部模拟动态的能力方面有了戏剧性的突破。这些新技术允许实时模拟，具有高精度和高效率，即使对远离平衡的系统也是如此。有了这些新功能，PI将研究各种链和梯形系统的谱函数。在大多数情况下，这些系统的精确、高分辨率的动力学特性以前是不可用的。此外，PI计划研究由链条和梯子组成的各种结，对于这些结，既没有进行基态模拟，也没有进行动力学模拟。将开发用于模拟稳态电流流动条件的新技术，并将其应用于结点。这些研究旨在为新一代由链和梯子组成的纳米级电子和自旋电子器件铺平道路。最近在二维模拟掺杂和受挫系统的能力方面也取得了重大进展，尽管算法尚未得到很好的表征或测试。为了在更简单的情况下开发和改进这些技术，它们将适用于梯子和交叉口。随后，改进技术的经验将应用于两个方面。成功地应用到两个维度将对理解铜酸盐超导体和相关材料产生重大影响。就更广泛的影响而言，这项工作将在许多不同的领域产生重大影响。其中最重要的领域之一是将数值和算法方面的知识从一个科学领域推广到另一个科学领域。PI已经并将继续努力将DMRG方法的使用推广到其他领域。最值得注意的是，PI已经开始在量子化学中使用DMRG，几个化学小组现在已经开始使用它。PI还致力于提高研究生和本科生在计算方法方面接受的培训水平。PI开发了几门新课程，包括研究生和本科生，向物理专业的学生介绍现代计算方法。其中几门课程已成为UCI课程的永久补充，国际PI将继续教授这些课程。PI还致力于在物理研究中鼓励更好的科学编程技术，包括维护一个可免费下载的高效C++矩阵库。非技术摘要：这项拨款主要支持对一维和二维强相互作用电子系统的性质的计算研究，如在纳米级设备中可能找到的。当电子被限制在这些小空间中时，当它们彼此非常接近时，它们的行为可以导致新的效应。这笔赠款支持开发描述这些类型的电子的计算技术的工作。除了发现和理解这些可能导致新器件的新特性外，开发的计算技术还将在其他研究领域得到广泛应用。这是在一个领域开发计算方法的力量，可以应用于许多其他应用。参与这项研究的学生将接受凝聚态物理和计算物理方面的出色培训。

This grant supports theoretical research on the properties of strongly interacting electron systems in low dimensions. In particular, the research will further develop algorithms associated with the density matrix renormalization group method so that this computational method can be applied to a wider variety of condensed matter systems and phenomena.One of the most exciting areas in condensed matter physics is the study of strong correlationeffects in low dimensional systems. These systems exhibit a wide range of behavior, such as hightemperature superconductivity, antiferromagnetism, striped, and spin liquid phases. They also show great promise, as fabrication techniques develop control on the nanoscale, for use in a new generation of electronic and spintronic devices. Numerical simulation techniques have become increasingly necessary to understand these systems, as the systems have strong coupling terms and competition between different types of order. The principal investigator (PI) is the creator of the density matrix renormalization group (DMRG), which is one of the most effective numerical techniques for studying strongly correlated systems. The PI and his group will apply DMRG to a variety of these systems, including spin chains, ladders, Y-junctions, both for pure spin systems and with hole doping.Understanding dynamical properties of these systems is essential for comparisons with experi-ments and for describing transport. Recently, there have been dramatic breakthroughs in the ability to simulate dynamics within DMRG. These new techniques allow for simulations in real time, with high accuracy and efficiency, even for systems far from equilibrium.With these new capabilities, the PI will study the spectral functions of a variety of chains andladder systems. In most cases, accurate, high-resolution dynamical properties for these systems have not been available previously. In addition, the PI plans to study a variety of junctions built out of chains and ladders, for which neither ground state nor dynamical simulation results have been performed. Novel techniques for simulating steady-state current flow conditions will be developed and applied to junctions. These studies are meant to pave the way for new generations of nano-scale electronic and spintronic devices built out of chains and ladders.There has also been recent major progress in the ability to simulate doped and frustrated systems in two dimensions, although the algorithms are not yet well characterized or tested. In order to develop and improve these techniques in a simpler context, they will be adapted to ladders and junctions. Subsequently, experience in improving the techniques will be applied to two dimensions. Successful application to two dimensions would have a major impact on the understanding of the cuprate superconductors and related materials.In terms of the Broader Impacts of this work, there will be significant impact in a number ofdifferent areas. One of the most important areas is the spreading of numerical and algorithm ad-vances from one area of science to another. The PI has worked and will continue to work to spread the use of the DMRG method to other fields. Most notably, the PI has initiated the use of DMRG in quantum chemistry, and several chemistry groups have now begun utilizing it. The PI is also working to improve the level of training both graduate and undergraduate students receive in computational methods. The PI has developed several new courses, both graduate and undergraduate, to introduce modern computational methods to physics students. Several of these courses have been made permanent additions to the UCI curriculum, and the PI continues to teach them. The PI is also working to encourage better scientific programming techniques in physics research, including maintaining a free downloadable highly efficient C++ matrix library.Non-Technical Abstract: This grant supports primarily computational research on the properties of strongly interacting systems of electrons in one-and two-dimensions as might be found in nano-scale devices. The behavior of electrons when they are confined in these small spaces and when they are very close to each other can lead to novel effects. This grant supports work that will develop computational techniques to describe these types of electrons. In addition to discovering and understanding these novel properties, which may lead to new devices, the computational techniques developed will find wide application in other fields of study. This is the power of developing computational methods in one field that can be applied to many other applications. Students involved in this research will receive excellent training in condensed matter physics and computational physics.