CAREER: Towards Predictive Modeling of Emergent Correlations and Dynamics in Strongly Interacting Quantum Matter

NONTECHNICAL SUMMARY

This CAREER award supports an integrated research, education, and outreach program in theoretical and computational condensed-matter physics. The main aim of the project is to advance our understanding of quantum matter composed of electrons that interact strongly with one another. These systems are at the heart of many fundamental physical phenomena, ranging from magnetism to superconductivity (flow of electrons with no resistance).

The problem at hand can be explained with an analogy from everyday life: one might learn to play individual musical notes yet not know how to put them together to produce a melody. Similarly, we now know the quantum-mechanical laws that govern individual electrons and nuclei but find it difficult to predict the emergent behavior of many such interacting components.

Just as a collection of atoms organizes itself into a solid, liquid, or gas depending on external conditions, electronic matter can exist in "valence-bond solid," "quantum spin liquid," or "Fermi gas" phases, among other possibilities. Reliably predicting the behavior of electronic systems will aid future technologies and searches for quantum materials with desirable properties.

The PI and his team will investigate geometrically "frustrated" magnetic materials found in nature and laboratories worldwide. Frustration arises when multiple spatial arrangements of electron "spin" orientations each have similar collective energy, so there is no clear winner. This feature results in unusual quantum dynamics that have been observed in modern-day experiments but for which theoretical explanations are limited.

Thus, a major focus of this proposal is to develop efficient computer algorithms to predict how such quantum materials behave under different conditions (change in temperature and application of a magnetic field) and how they respond to external probes (involving light or neutrons). The PI and his team will also employ existing state-of-the-art numerical methods to address outstanding fundamental questions associated with this class of magnetic materials.

The PI's education and outreach programs are synergistically coupled to his research. The focus is on communicating the workings of computational methods for quantum systems to graduate students and the wider research community. With input from expert authors, the PI and his team will write an e-book that will train the next generation to embrace a rapidly evolving lexicon of quantum-mechanical concepts.

Through multiple outreach activities at his home institution, including open houses and public seminars, the PI will convey the importance of quantum physics in our everyday lives. To inspire more students to pursue higher education and careers in science, the PI will conduct tutoring and mentoring activities at a local K-12 school that enrolls a large number of students from underrepresented minority groups.

TECHNICAL SUMMARY

This CAREER award supports an integrated research, education, and outreach program in theoretical and computational condensed-matter physics. The main aim of the project is to advance our understanding of strongly correlated quantum systems, those not approximated by a non-interacting model of electrons. Reliably predicting their behavior from computer simulations remains a major challenge in physics, chemistry, and materials science.

Additionally, the quantum mechanics of correlated systems in the time domain, central to both equilibrium and non-equilibrium phenomena, is not as well-characterized and understood as its time-independent counterpart. Many experiments collect a wealth of dynamical information, but one needs theoretical inputs to interpret them. For example, evidence for fractionalized spinons in one dimension is indirectly inferred from comparison of neutron scattering data and theory.

The PI and his team will investigate geometrically frustrated magnets, which harbor valence-bond-solid, quantum-spin-liquid, and spin-nematic phases. Efforts in this area will further the PI's goal of predicting properties such as transition temperatures, magnetization profiles, and dynamical responses, given minimal knowledge of the quantum material.

The PI and his team will perform research in the following directions:

1. They will numerically simulate and analyze spin dynamics at zero and finite temperature for spin-orbit-coupled, spin-ice, and spin-1 magnets on kagome and pyrochlore lattices in an applied magnetic field. Comparisons to measurements from dynamical probes such as inelastic neutron scattering and terahertz spectroscopy experiments will be carried out.

2. They will explore a toy lattice model of frustration that harbors "three-colored" exact ground states. The model offers a way to understand non-equilibrium dynamical phenomena (such as glassiness) and has potential pedagogical value.

3. They will develop the "density-matrix-downfolding" technique, a form of Hilbert-space operator renormalization, to generate effective Hamiltonians. This method will help connect real materials to strongly-correlated lattice models.

The PI's education program will focus on communicating the workings of computational methods for quantum systems to graduate students and the wider research community. With input from expert authors, the PI and his team will write an e-book focused on many-body-wavefunction and density-matrix based approaches. Through multiple outreach activities at his home institution, including open houses and public seminars, the PI will convey the importance of quantum physics in our everyday lives.

To inspire more students to pursue higher education and careers in science, the PI will conduct tutoring and mentoring activities at a local K-12 school that enrolls a large number of students from underrepresented minority groups.

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.