Simulation studies of ground state phases and criticality in correlated quantum matter

该奖项支持计算量子多体物理学的研究和相关教育活动，重点是自旋系统中的集体量子现象。量子自旋系统是描述莫特绝缘体磁性能的重要模型。除了在实验研究材料的直接建模中发挥重要作用外，量子自旋模型还可以用作简化的原型模型，用于捕获当前正在进行的理论和计算研究的各种多体现象的基本物理。该奖项的主要目标是通过无偏计算机模拟，主要使用量子蒙特卡罗方法，获得对集体量子多体态物理学的新的一般见解。特别感兴趣的是量子相变，在零温度下发生的相变与相关的标度行为也在有限温度下发生，作为调节系统中量子涨落强度的某些模型参数的函数。PI设计了一类自旋- 1 / 2晶格系统，其中标准的反铁磁海森堡交换相互作用被设计成破坏反铁磁秩序的多自旋相互作用所补充。这种二维跃迁可能与初等激发的分数化有关。通常，尼尔态的激发是携带自旋1的自旋波，而在价键固态中，存在自旋1的间隙“三子”激发。然而，在接近相变的情况下，先前的分析和数值研究表明，这些激发可能会分形成携带1 / 2自旋的自旋子。这种自旋子的定义对相变的理论描述和相变的实验特征都有深远的影响。自旋子可能在许多强相关电子系统中发挥重要作用，例如在低掺杂高tc超导体的“奇怪金属”状态中。PI正在进行量子蒙特卡罗研究，以表征自旋子的性质及其在物理观测中的表现。原始系统和无序系统都被考虑。新的和改进的模拟方法的工作将作为该奖项的一个组成部分进行。通过该奖项开发的方法有助于新兴的软件“工具箱”，可以模拟莫特绝缘体的磁性。这些方法具有更广泛的适用性，超出了主要的科学问题的解决，并在其他领域感兴趣，例如研究超冷原子在光学晶格和量子信息理论。该奖学金资助的研究生将接受有关这些先进方法及其应用的培训。PI还积极地在暑期学校教授研究生和博士后研究人员，同时也在开发学习量子蒙特卡罗模拟和其他数值多体技术的在线教学材料。该奖项支持量子自旋模型的计算机模拟研究和相关教育活动。这些相互作用的微观磁矩系统代表了某些电绝缘材料中单个原子或分子上的电子。根据材料的晶体结构和化学成分，可以实现各种磁性能。该奖项的目的是进行计算机模拟研究，以帮助其他研究人员进行实验调查，以及研究模型系统的基本方面，以进一步了解原则上可能实现的性质。这些模拟与现有的分析理论有关，并影响发展中的理论概念。与日常生活中物质的三种常见相——液体、固体和气体——类似，一个由大量电子自旋组成的系统也可以来自不同的相。可能性是非常丰富的，有许多不同的阶段类似于三个常见的阶段。自旋可以“固化”成单个电子磁矩或磁矩对形成各种规则模式的状态。这些模式可以在相变中“融化”，在相变中出现新的类似液体的自旋态。无论是从基础科学的角度还是从涉及电子自旋特殊性质的最终技术应用的角度来看，理解这些量子相和量子相变都是非常具有挑战性和重要的。PI先前开发了计算方法，并设计了一类自旋模型，其中某些磁量子相变可以以前所未有的细节进行研究。PI将研究接近量子相变的自旋系统的基本激发的性质。激发可以看作是作为波在系统中传播的缺陷。这些波携带一定数量的磁矩，通常有一个最小的磁矩单位。一个令人兴奋的可能性，实验和理论结果，是这个最小的单位可以分裂成两个独立传播的波。PI正在研究模型系统中的这些自旋子。从计算机模拟中获得的信息将为这些有趣的量子实体的特性以及它们在各种情况下所扮演的角色提供独特的见解。新的和改进的计算方法将发展到这项研究。这些计算工具将有助于计算量子物理的软件基础设施。该奖项支持的研究生正在开发先进模拟方法和多体量子物理方面的专业知识。PI还积极参与各种其他教育活动，包括在国际暑期学校讲课和编写在线教学材料，以学习与该奖项有关的先进计算技术。

TECHNICAL SUMMARYThis award supports research and related educational activities in computational quantum many-body physics, with a focus on collective quantum phenomena in spin systems. Quantum spin systems are important models for describing the magnetic properties of Mott insulators. In addition to their important role in direct modeling of experimentally studied materials, quantum spin models can also be used as simplified prototypical models capturing essential physics of various many-body phenomena that are currently subjects of ongoing theoretical and computational investigations. The main objective of this award is to gain new generic insights into the physics of collective quantum many-body states through unbiased computer simulations, primarily using quantum Monte Carlo methods. Of particular interest are quantum phase transitions, phase transitions that take place at zero temperature with associated scaling behavior also at finite temperature, as a function of some model parameter that regulates the strength of the quantum fluctuations in the system. The PI has devised a class of spin-one-half lattice systems in which the standard antiferromagnetic Heisenberg exchange interaction is supplemented by multi-spin interactions engineered to destroy the antiferromagnetic order. This transition in two dimensions may be associated with fractionalization of elementary excitations. Normally, the excitations of the Neel state are spin waves carrying spin one, and in the valence-bond-solid state there are gapped spin-one "triplon" excitations. However, close to the phase transition, previous analytical and numerical studies indicate that these excitations may fractionalize into spinons carrying spin-one-half. This deconfinement of spinons has far reaching consequences both for the theoretical description of the phase transition and for experimental signatures of it. Spinons may play an important role in many strongly-correlated electron systems, for example in the "strange metal" state of underdoped high-Tc superconductors. The PI is carrying out quantum Monte Carlo studies in order to characterize the nature of the spinons and their manifestations in physical observables. Both pristine and disordered systems are considered. Work on novel and improved simulation methods will be carried out as an integral part of the award. The methods to be developed through this award are contributing to the emerging "toolbox" of software enabling simulations of magnetic properties of Mott insulators. These methods have broader applicability, beyond the main scientific questions addressed, and are of interest in other fields, for example studies of ultracold atoms in optical lattices and in quantum information theory. Graduate students supported by this award will receive training in these advanced methods and their applications. The PI is also actively teaching graduate students and postdoctoral researchers at summer schools, and is also developing on-line instructional material for learning quantum Monte Carlo simulations and other numerical many-body techniques.NON-TECHNICAL SUMMARYThis award supports research and related educational activities in computer simulation studies of quantum spin models. These systems of interacting microscopic magnetic moments represent electrons localized at individual atoms or molecules in certain electrically insulating materials. Various magnetic properties can be achieved, depending on the crystal structure and the chemical composition of the material. The objective of the award is to carry out computer simulation studies to aid experimental investigations carried out by other researchers, as well as to study fundamental aspects of the model systems to gain further insights into what kind of properties are possible to achieve in principle. These simulations relate to existing analytical theories and influence developing theoretical concepts. In analogy with the three common phases of matter encountered in daily life - liquid, solid, and gas - a system of a large number of electronic spins can also from different phases. The possibilities are very rich, with many different phases analogous to the three common ones. Spins can "solidify" into states in which the individual electronic magnetic moments or pairs of moments form various regular patterns. These patterns can "melt" at phase transitions where new liquid-like spin states appear. Understanding these quantum phases and quantum phase transitions is very challenging and important, both from a fundamental scientific perspective and for ultimate technological applications involving the special properties of electronic spins. The PI has previously developed computational methods and devised a class of spin models in which certain magnetic quantum phase transitions can be studied in unprecedented detail. The PI will study the nature of the elementary excitations of spin systems close to quantum phase transitions. An excitation can be thought of as a defect propagating as a wave through the system. These waves carry certain amounts of magnetic moment and normally there is a smallest unit of it. An exciting possibility with both experimental and theoretical consequences, is that this smallest unit can split up into two independently propagating waves. The PI is investigating these spinons in model systems. Information gained from computer simulations will give unique insights into the properties of these intriguing quantum entities and the role they play in various circumstances. New and improved computational methods will be developed to this research. These computational tools will contribute to the software infrastructure of computational quantum physics. Graduate students supported by the award are developing expertise in advanced simulation methods and many-body quantum physics. The PI is also actively involved in various other educational activities, including lecturing at international summer schools and developing pedagogical on-line material for learning the advanced computational techniques related to the award.