Navigating Frustration

技术总结该奖项支持有关受挫系统的理论研究和教育。PI旨在了解如何处理S=1和S=3/2的自旋，以及如何找到由于无序而产生的局部自由度。研究有四个方面：1方法--拟退化密度矩阵和/或Renyi熵方法将被用来表征涌现的局部自由度。我们将发展局域相关的变分波函数来模拟缺乏平移不变性的量子系统的基态。用变分蒙特卡罗方法研究了Kagome和焦绿石晶格上的高度受挫反铁磁体--Kagome和焦绿石晶格上的自旋1反铁磁体。有效哈密顿方法将被应用于具有随机通量的情况，既可以找到Kagome晶格上自旋与电子耦合的相图，也可以在大N Schwinger玻色子理论中找到自旋1/2焦绿石反铁磁体的正确基态。无序和挫折-PI旨在解决Bethe晶格上渗流时自旋1/2反铁磁体的三个主要谜团：(1)为什么浮现的自旋自由度解耦？(2)长程有序是完全由它们传播的吗？(3)最小能隙尺度如何与系统大小有关？4.相互作用费米子-精确对角化和解析方法将被用来解码有趣的规律的“重合幅度”波函数。PI将开发的方法很可能对任何具有无序的材料有用。在介绍性文本之后，PI正在完成一篇关于固态物理的研究生文本，但没有场论，这是一个教学上的中间地带，希望这将适合从事量子材料工作的实验者。PI将包括本科生参与研究。非技术总结该奖项支持关于受挫材料的理论研究和教育。“受挫”是一个术语，指的是当电子在固体中的原子之间跳跃，或者“自旋”，当电子没有跳跃时，电子发出相互冲突的信号时发生的事情。自旋是电子本征磁性的抽象。受挫体系的一个特点是：不是有一个明显受到互动支持的单一集体国家，而是有许多同样在技术措施上表现良好的集体国家。因此，通常被忽视的小交互可能会打破平衡，有利于这些状态中的特定一种。或者，当量子力学很重要时，这些态的量子叠加可能会产生，在某些情况下，这样的集体态具有奇异的性质，例如具有分数电荷的出射“粒子”。PI的目标是找到在这些州中“导航”的方法。在许多真实材料中，为受挫模型定义规则的规则晶格被“稀释”，即缺少一个偶然的位置。在一个受挫的系统中，这可能会产生戏剧性的影响。PI将完成一项正在进行的研究，该研究不包括挫折感，但将量子力学与稀释到渗流阈值相结合，在渗流阈值中，相互作用的自旋网络由于被移除的位置而处于断开的边缘。PI将采用一种计算方法来研究游戏规则统一但受挫的系统中可能的非均匀状态。将开展几个解决稀释问题的项目。PI的目标是采用各种数值方法。例如，被称为“纠缠”的量是衡量一个系统拥有多少量子信息的量度。这可能是识别系统所处紧急状态的一种强有力的方法。PI将评估一个小区域相对于其周围环境的纠缠，并评估这是否可以用来识别由于稀释而出现在该区域的哪种新出现的局部自由度。PI将开发的方法可能对任何具有无序的材料有用。在介绍性文本之后，PI正在完成一篇关于固态物理的研究生文本，但没有场论，这是一个教学上的中间地带，希望这将适合从事量子材料工作的实验者。PI将让本科生参与这项研究。

TECHNICAL SUMMARYThis award supports theoretical research and education on frustrated systems. The PI aims to understand how to handle spins S = 1 and S = 3/2, and how to find emergent local degrees of freedom due to disorder. The research has 4 thrusts:1 Methods - The methods of quasi-degenerate density matrix and/or Renyi entropy will be applied to characterize emergent local degrees of freedom. Locally-dependent variational wavefunctions will be developed to model the ground states of quantum systems lacking translational invariance.2. Highly frustrated antiferromagnets - The spin-1 antiferromagnet on kagome and pyrochlore lattices will be studied, using variational Monte Carlo, also by DMRG using the loop-free cactus lattice as an ersatz. The effective Hamiltonian approach will be applied to situations with random fluxes, both to find the phase diagram of spins coupled to electrons on the kagome lattice, and also to find the correct ground state for spin-1/2 pyrochlore antiferromagnet in the large-N Schwinger boson theory.3. Disorder and frustration - The PI aims to resolve the three major mysteries about the spin-1/2 antiferromagnet at percolation on the Bethe lattice: (1) Why do the emergent spin degrees of freedom decouple? (2) Is the long-range order propagated purely by them? (3) How does the smallest gap scale with system size?4. Interacting fermions - Exact diagonalization and analytic methods will be used to decode the intriguing regularities of the 'coincident amplitude' wavefunctions. The methods the PI will develop will likely be useful for any material with disorder. The PI is completing a graduate text on solid state physics after the introductory texts, but without field theory, a pedagogical middle ground which hopefully will be congenial to experimentalists working on quantum materials. The PI will involve undergraduate students in the research.NONTECHNICAL SUMMARYThis award supports theoretical research and education on frustrated materials. "Frustration" is the technical term for what happens when either electrons which may hop between atoms in a solid, or "spins," which are abstractions of the intrinsic magnetism of electrons, when the electrons don't hop, give conflicting signals to each other. A hallmark of a frustrated system is: rather than having a single collective state which is obviously favored by the interactions, there are numerous collective states which are equally good by technical measures. As a result, small interactions that are usually ignored might tip the balance and favor a particular one of these states. Or, when quantum mechanics is important, a quantum superposition of these states may result, and in some cases such a collective state has exotic properties, such as emergent "particles" having fractional charge. The PI aims to find ways to "navigate" through these states. In many real materials the regular lattice defining the rules for a frustrated model is "diluted" i.e. missing an occasional site. This may have dramatic effects in the case of a frustrated system. The PI will complete an ongoing study that does not include frustration, but combines quantum mechanics with dilution to the percolation threshold, where the network of interacting spins is on the verge of becoming disconnected due to the removed sites. The PI will adapt a computational method study possible non-uniform states in systems where the rules of the game are uniform, but frustrated. Several projects which address dilution will be pursued.The PI aims to adapt a variety of numerical methods. For example, the quantity called "entanglement" which is a measure of how much quantum information a systems has. This can be a powerful way to identify the kind of emergent state the system is in. The PI will evaluate the entanglement of a small region relative the environment that surrounds it and evaluate whether this can be used to identify which kind of emergent local degree of freedom is appearing in that region because of dilution.The methods the PI will develop will likely be useful for any material with disorder. The PI is completing a graduate text on solid state physics after the introductory texts, but without field theory, a pedagogical middle ground which hopefully will be congenial to experimentalists working on quantum materials. The PI will involve undergraduate students in the research.