Navigating Frustration

技术总结该奖项支持理论研究和教育受挫的系统。PI的目的是了解如何处理自旋S = 1和S = 3/2，以及如何找到由于无序而出现的局部自由度。本文的研究工作主要有以下四个方面：1方法--拟退化密度矩阵和Renyi熵的方法将被用来刻画涌现的局部自由度。局域相关的变分波函数将被发展来模拟缺乏平移不变性的量子系统的基态.高阻挫反铁磁体-自旋1反铁磁体的kagome和烧绿石晶格将进行研究，使用变分蒙特卡罗，也通过DMRG使用无环仙人掌晶格作为一个ercurrency。有效哈密顿量方法将被应用到具有随机通量的情况下，既可以找到kagome晶格上的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为1/2的烧绿石反铁磁体的正确基态。无序和挫折-PI的目的是解决三个主要的奥秘自旋1/2反铁磁体在渗流的贝特晶格：（1）为什么出现的自旋自由度去耦？(2)长序纯粹是由它们传播的吗？(3)最小间隙如何随系统大小而变化？4.相互作用的费米子-精确的对角化和分析方法将被用来解码有趣的“重合振幅”波函数。PI将开发的方法可能对任何具有障碍的材料都有用。PI在介绍性文本之后正在完成固态物理学的研究生文本，但没有场论，这是一个教学的中间地带，希望能与从事量子材料研究的实验学家相适应。PI将让本科生参与研究。NONTECHNICAL SUMMARY该奖项支持理论研究和对挫折材料的教育。“挫折”是一个技术术语，指的是当电子在固体中的原子之间跳跃时，或者当电子不跳跃时，电子的内在磁性的抽象“自旋”，相互发出冲突的信号。一个受挫折的系统的一个标志是：不是有一个单一的集体状态，这显然是有利于相互作用，有许多集体状态，同样好的技术措施。因此，通常被忽略的小的相互作用可能会打破平衡，有利于这些状态中的一个。或者，当量子力学很重要时，这些状态的量子叠加可能会产生，在某些情况下，这样的集体状态具有奇异的性质，例如具有分数电荷的新兴“粒子”。 PI旨在找到在这些状态中“导航”的方法。 在许多真实的材料中，为受抑模型定义规则的规则晶格是“稀释的”，即缺少偶尔的位点。 这可能会在一个失败的系统的情况下产生戏剧性的影响。PI将完成一项正在进行的研究，该研究不包括挫折，但将量子力学与稀释结合到渗透阈值，其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失败的系统中可能的非均匀状态。几个解决稀释问题的项目将继续进行。PI旨在适应各种数值方法。 例如，被称为“纠缠”的量，它是衡量一个系统拥有多少量子信息的一个指标。这可能是一个强有力的方法来识别系统所处的紧急状态。 PI将评估一个小区域相对于周围环境的纠缠度，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涌现的局部自由度。PI将开发的方法可能对任何无序材料都有用。PI在介绍性文本之后正在完成固态物理学的研究生文本，但没有场论，这是一个教学的中间地带，希望能与从事量子材料研究的实验学家相适应。PI将让本科生参与研究。

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.