Entanglement Physics of Quantum f-electron Materials

NONTECHNICAL SUMMARY

This award supports theoretical research and education in condensed matter physics, in the subfield of f-electron physics and quantum matter.

The behavior of matter on atomic scales is governed by quantum mechanics, which describes the motion of particles as a wave, evolving according to the Schrodinger wave equation. While the application of this equation to isolated electrons is fully understood, the corresponding many-body version of this equation that governs the collective quantum behavior of electrons inside matter is far too complex to be solved in detail. The astronomical scale of this complexity may be grasped by noting that the number of electrons in a pound of iron is larger than the number of stars in the known universe.

One of the strange manifestations of quantum mechanics is a phenomenon known as entanglement, whereby remote electrons in a material intimately correlate their motion. The unexpected collective behavior of electrons that results from this entanglement has the capacity to endow quantum matter with emergent properties, such as magnetism, superconductivity, or superfluidity, and many more that are presumably not yet discovered. The quest to understand and manipulate these emergent properties, and to relate them to the underlying quantum mechanics is a key goal of modern condensed matter physics.

The award supports research in the area of f-electron materials, a unique class of metals that can be fine-tuned to the brink of magnetism where they develop a special quantum state called a 'Quantum Critical Point'. Quantum critical points can be thought of as a kind of electronic stem cell - a state of matter that can easily transform itself into a broad class of novel quantum phases, such as unconventional superconductors. By developing a new mathematical description of these quantum critical points and the phases they can transform into, the PI aims to gain a new understanding of the physics of quantum materials.

Graduate students and postdocs will be involved in an essential way in the research, and will be mentored and trained in a broad range of theoretical techniques. The PI also plans to write a popular book introducing the frontier of quantum condensed matter physics to non-experts.

TECHNICAL SUMMARY

This award supports theoretical research and education in condensed matter physics, in the subfield of f-electron physics. The research has three main subheadings:

1) New approach to quantum criticality: Using a new Schwinger boson method, and working in conjunction with experimentalists, the research team will develop a theory of ferromagnetic quantum criticality in heavy-electron materials. This work will be extended to antiferromagnets and will be used to compute the generalized phase diagram of heavy fermions. The research team will develop a theory for the co-existence of magnetism and the Kondo effect. By extending early work of Larkin and Pikin, the research will develop a theory for the quantum annealing of finite-temperature first-order phase transitions into quantum critical points at absolute zero.

2) Analytic-computational approach to entanglement & novel order in rare-earth materials: Working with theorists at the Flatiron Institute, New York, the research team will apply Matrix Product State approaches to simple one- and two-dimensional Kondo lattices, focusing on the low-entanglement case of the Kondo insulator, using these methods to establish and explore the composite nature of heavy fermions.

3) A new approach to Raman and Photoemission phenomenology: Generalizing the theory of optical lattices to crystal fields, the research will develop a theory of the Raman interaction of light with crystal-field levels in f-electron materials. A new criterion for measuring the degree of localization of f-electrons using angle-resolved and core-level x-ray photoemission will be developed.

Graduate students and postdocs will be involved in an essential way in the research, and will be mentored and trained in a broad range of theoretical techniques. The PI also plans to write a popular book introducing the frontier of quantum condensed matter physics to non-experts.

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.