CAREER: Theoretical and Numerical Investigation of Symmetric Mass Generation

非技术总结这个职业奖项支持探索新的量子机制的研究和教育活动，这些机制通过增加此类材料中电子之间的相互作用强度将金属转变为绝缘体。在固态物理学中，电子结构理论为金属和绝缘体提供了标准的描述，使得最高能量的电子位于金属的能带内，或者在禁带内，就像绝缘体的情况一样。在这个理论中，材料从金属到绝缘体的转变对应于电子能谱中的带隙开放，这总是需要改变材料的对称性来改变其能带结构。这项研究旨在研究一种超越标准电子结构理论的金属到绝缘体转变的不同机制，在这种机制中，电子的相互作用和随后的相关运动起着核心作用。这种新的机制被称为对称质量产生，它在电子多体能谱中打开了一个激发能隙，而不会改变对称性质--这一现象无法用标准的电子结构理论来解释。理解这种新的机制可能会对凝聚态物理中物质的量子相进行分类，以及在高能物理中理解基本质粒子的质量起源具有重要意义。这个项目将研究对称质量产生，目的是解决：(1)如何设计适当的相互作用来实现这种现象，(2)当金属成为绝缘体时到底发生了什么，(3)这种新型绝缘体区别于传统带状绝缘体的独特实验特征是什么。教育活动的重点是留住LGBT+(女同性恋者、男同性恋者、双性恋者、变性人和其他性别和性少数)的物理学学生，为他们提供研究机会，并提高LGBT+在校园中的知名度。这一努力将建立一个更多样化和包容性的学术环境，吸引有才华的未得到服务的学生进入物理学，并有助于发展一支多样化的、具有全球竞争力的科学劳动力队伍。技术总结该职业奖支持研究和教育活动，以研究相互作用的量子多体系统中费米子的能隙打开(质量生成)的新机制，称为对称质量生成。这种机制是一种非微扰相互作用驱动的能隙打开效应，不能解释为单粒子能带结构的变化。对称质量的产生为凝聚态物理中超越电流带理论的金属-绝缘体跃迁提供了一种新的机制，也为超越标准希格斯机制的费米子质量提供了新的来源。这一研究有助于加深对相互作用的拓扑绝缘子的理解，并转化关于质量产生的前沿知识。这项研究将探索三个相关方面：(1)设计合适的相互作用以实现对称质量产生绝缘相的原则，(2)对称质量产生相互作用下缝隙-开口跃迁的普遍性质，(3)掺杂对称质量产生绝缘体的效应以及在费米液体中费米表面实现对称质量产生的可能性。这项研究将结合场论，例如范畴对称性、对偶、单极标度和降维，以及数值模拟，例如机器学习辅助的变分蒙特卡罗方法，来解决关于对称质量产生的科学问题。这一研究成果将推进手征费米子相互作用拓扑相、强关联材料和晶格正则化等方面的知识前沿。教育活动的重点将是支持和留住LGBT+(女同性恋者、男同性恋者、双性恋者、变性人和其他性别和性少数群体)物理学本科生，并为各级LGBT+学生/研究人员建立一个欢迎当地社区。这些目标将通过(1)向目标群体提供指导研究机会和(2)为加州大学圣地亚哥分校物理系LGBT+学生/研究人员发起和组织每周茶点社交活动来实现。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 CAREER award supports research and educational activities to explore novel quantum mechanisms that transform metals into insulators by increasing the interaction strength between electrons in such materials. In solid-state physics, the electronic structure theory provides the standard description for metals and insulators, such that the highest-energy electrons lie within an energy band for metals or in the band gap, a forbidden zone, as is the case for insulators. In this theory, transforming material from metal to insulator corresponds to a band gap opening in the electron energy spectrum, which always requires a change in the symmetry properties of the material to modify its band structure. This research aims to study a different mechanism for the metal-to-insulator transformation that is beyond the standard electronic structure theory in which the interaction and subsequent correlated motion of the electrons play the central role. The novel mechanism is called symmetric mass generation, which opens an excitation gap in the electron many-body energy spectrum without any change of symmetry properties — a phenomenon that is not explained by standard electronic structure theory. Understanding this novel mechanism may have implications in classifying quantum phases of matter in condensed matter physics and understanding the origin of mass for fundamental matter particles in high-energy physics. This project will investigate symmetric mass generation with an aim to address: (1) how appropriate interactions can be designed to realize this phenomenon, (2) what happens precisely as the metal becomes an insulator, (3) what are the unique experimental signatures of the novel insulator that distinguish it from conventional band insulators. The educational activity focuses on retaining LGBT+ (lesbian, gay, bisexual, transgender, and other gender and sexual minorities) students in physics by providing them with research opportunities and increasing LGBT+ visibility on campus. The effort will build a more diverse and inclusive academic environment that attracts talented under served students to physics and contribute to developing a diverse and globally competitive workforce in science.TECHNICAL SUMMARYThis CAREER award supports research and educational activities to study a novel mechanism for the gap opening (mass generation) of fermions in interacting quantum many-body systems, called the symmetric mass generation. The mechanism is a non-perturbative interaction-driven gap-opening effect that cannot be interpreted as a change in the single-particle band structure. Symmetric mass generation provides a new mechanism for metal-insulator transition beyond current band theory in condensed matter physics and a new origin for fermion mass beyond the standard Higgs mechanism. This research can advance the understanding of interacting topological insulators and transform the frontier knowledge about mass generation. The research will explore three related aspects: (1) the principle of designing appropriate interaction to realize the symmetric mass generation insulating phase, (2) the universal properties of the gap-opening transition under the symmetric mass generation interaction, and (3) the effect of doping symmetric mass generation insulators and the possibility to realize symmetric mass generation on the Fermi surface in a Fermi liquid. The research will combine field theory, for example, categorical symmetry, duality, monopole scaling, and dimension reduction, and numerical simulation, for example machine-learning-assisted variational Monte Carlo methods, to tackle scientific problems about symmetric mass generation. The research outcome will advance the knowledge frontier of interacting topological phases, strongly correlated materials, and lattice regularization for chiral fermions. The educational activities will focus on supporting and retaining LGBT+ (lesbian, gay, bisexual, transgender, and other gender and sexual minorities) undergraduates in physics and building a welcoming local community for LGBT+ students/researchers at all levels. These objectives will be attained by (1) providing mentored research opportunities to the targeted group and (2) initiating and organizing a weekly tea-time social event for LGBT+ students/researchers in Physics Department at UCSD.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.