CAREER: Theoretical and Numerical Investigation of Symmetric Mass Generation

University Of California-San Diego, La Jolla CA

Investigators

Abstract

NONTECHNICAL SUMMARY This 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 will expand access to research-based training and mentoring and will provide mentored research opportunities, strengthen peer and faculty mentoring networks, and support regular community-building activities for students and researchers at different career stages. These activities will be open to all undergraduate students in physics and are designed to improve student retention, and preparation for STEM careers, thereby contributing to a strong and globally competitive U.S. science and engineering workforce. TECHNICAL SUMMARY This 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. 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.