Collaborative Research: Worm Algorithm and Diagrammatic Monte Carlo for Strongly Correlated Condensed Matter Systems

非技术总结该奖项支持理论和计算研究，旨在促进对电子相互作用强烈的材料的基本理解。这些材料表现出不同寻常的特性和现象，可能导致未来的器件技术。PI将使用他们开发的先进计算方法来对这类材料中的电子进行计算机模拟，并探索在非常低的温度和中等压力下，一个概念上相关的强相互作用粒子-氦原子系统的性质。该团队将使用简化的模型来研究具有强相互作用电子的材料中如何发生超导电性。超导性是一种物质的量子状态，电子在其中协同作用。其结果是，处于超导状态的电子可以在没有阻力的情况下流动，这与铜和制造加热元件的金属不同。该团队还将研究电子的新状态，这些状态是由于它们与晶格的振动相互作用而出现的。该团队将进一步研究强相互作用电子与晶格振动相互作用的后果，并研究晶体受光照射时出现的新状态。该项目的另一个重点是氦，这是第二种最轻的元素，在室温下处于气相中。在极低的温度下，氦变成一种液体，可以被认为是一个强相互作用的电子系统，但不带电荷。当压力超过大气压的25倍时，它就会变成结晶固体，就像液体一样，表现出与量子力学原理一致的耐人寻味的性质，这些原理适用于许多相互作用的粒子系统。在足够低的温度下，液氦进入一种被称为超流态的状态，这类似于超导电性。该团队将探索由于量子力学和氦原子的轻质量而产生的不完美氦晶体的惊人特性。其中包括氦原子在固体中的无摩擦传输，以及在实验中观察到的令人费解的塑性现象，目前尚无令人满意的理论解释。研究团队处于有利地位，能够在这些具有基本和技术兴趣的挑战性问题上推进知识，部分原因是他们开发的计算工具非常适合研究具有强相互作用粒子的系统，例如某些类别材料中的电子和在极低温度和中等压力下的氦原子。该项目还支持培训研究生和博士后研究人员先进的数值技术、量子统计、凝聚态和原子物理的主题问题，以及高性能计算。该项目还有助于推进精密多体物理倡议，该倡议旨在促进在尖端研究方面的国际合作，以了解包括量子物质在内的物质的集体性质。在此背景下计划的活动包括：两个主要的国际研讨会，在美国物理学会3月份会议上的重点会议，以及在UMassAmherst举行的专题小型研讨会。该奖项支持理论和计算研究，旨在通过使用两种最先进的第一原理方法来实现对各种凝聚态系统的电子和传输性质的基本了解：WORM算法(Wa)和图解蒙特卡罗(DiagMC)，这两种方法都是由研究团队介绍的。该项目的主要目标是：(I)关联电子原型模型中库珀不稳定性的诊断MC研究：具有库仑和电子-声子相互作用的系统以及排斥费米-哈伯德模型。(Ii)新极化子态的诊断MC研究。(Iii)基于WA的He-4固体无序诱导量子物理研究。该项目还支持对研究生和博士后研究人员进行高级数值技术、量子统计、凝聚态和原子物理的主题问题以及高性能计算方面的培训。该项目还有助于推进精密多体物理倡议，该倡议旨在促进在尖端研究方面的国际合作，以了解包括量子物质在内的物质的集体性质。在此背景下计划的活动包括：两个主要的国际研讨会，在美国物理学会3月份会议上的重点会议，以及在马萨诸塞州大学阿默斯特分校举行的专题迷你研讨会。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical and computational research with an aim to advance fundamental understanding of materials in which electrons interact strongly with each other. These materials exhibit unusual properties and phenomena which may lead to future device technologies. The PIs will use advanced computational approaches they have developed to perform computer simulations of electrons in this class of materials, and to explore the properties of a conceptually related system of strongly interacting particles - helium atoms at very low temperatures and modest pressure. The team will use simplified models to investigate how superconductivity can occur in materials with strongly interacting electrons. Superconductivity is a quantum state of matter where the electrons act in concert. A consequence is that electrons in a superconducting state can flow without resistance, unlike those in copper and the metals from which heating elements are made. The team will also investigate novel states of electrons that emerge due to their interaction with the vibrations of the crystalline lattice. The team will further pursue the consequences of interactions of strongly interacting electrons with crystalline lattice vibrations and investigate novel states that emerge when crystals are illuminated by light. Another focus of the project is helium, the second lightest element, which is in gas phase at room temperature. At extremely low temperatures helium becomes a liquid that can be thought of as a strongly interacting system of electrons, but without charge. At pressures above 25 times the atmospheric pressure, it becomes a crystalline solid and, like the liquid, displays intriguing properties consistent with the principles of quantum mechanics applied to systems of many interacting particles. At sufficiently low temperatures, liquid helium enters a state, called superfluidity, which is the analog of superconductivity. The team will explore striking properties of imperfect crystals of helium that arise as a consequence of quantum mechanics and the light mass of helium atoms. These include the frictionless transport of helium atoms through the solid and puzzling plastic phenomena observed in experiments for which no satisfactory theoretical explanations currently exist. The research team is well positioned to advance knowledge in these challenging problems of fundamental and technological interest, in part because the computational tools they have developed are well suited for the investigation of systems with strongly interacting particles, such as electrons in some classes of materials and helium atoms at extremely cold temperatures and modest pressures.This project also supports training graduate student and post-doctoral researchers in advanced numerical techniques, quantum statistics, topical problems of condensed-matter and atomic physics, and high-performance computing. This project also helps to advance the Precision Many Body Physics Initiative which is aimed to facilitate international collaboration in cutting edge research directed toward understanding collective properties of matter, including quantum matter. Activities planned within this context include: two major international workshops, Focused Sessions at American Physical Society March Meetings, and topical mini workshops at UMass Amherst.TECHNICAL SUMMARYThis award supports theoretical and computational research aimed at achieving a fundamental understanding of electronic and transport properties of a variety of condensed matter systems through the use of two state-of-the-art first-principles approaches to correlated quantum many-body systems: Worm Algorithm (WA) and Diagrammatic Monte Carlo (DiagMC); both introduced by the research team. The main goals of the project are: (i) DiagMC studies of Cooper instability in prototypical models of correlated electrons: systems with Coulomb and electron-phonon interactions and the repulsive Fermi-Hubbard model. (ii) DiagMC study of novel polaron states. (iii) WA-based study of disorder-induced quantum physics in solid He-4. (iv) WA-based study of novel exciton-photonic cooperative phases.This project also supports training graduate student and post-doctoral researchers in advanced numerical techniques, quantum statistics, topical problems of condensed-matter and atomic physics, and high-performance computing. This project also helps to advance the Precision Many Body Physics Initiative which is aimed to facilitate international collaboration in cutting edge research directed toward understanding collective properties of matter, including quantum matter. Activities planned within this context include: two major international workshops, Focused Sessions at American Physical Society March Meetings, and topical mini workshops at UMass Amherst.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.