CAREER: Solving the Quantum Many-Body Problem in Moire Materials with Quantum Geometry & Tensor Networks

About This Grant

NONTECHNICAL SUMMARY So-called "emergent" behavior occurs when a large number of particles act together in concert to produce phenomena that are not possible with individual particles. A fascinating example occurs in quantum mechanical systems with a large number of electrons, such as semiconductors. Each electron carries one unit of electric charge and cannot be split. However, under certain conditions, quantum effects conspire to produce emergent particles called “anyons” that each carry a fraction of an electric charge. This striking phenomenon provides a potential platform to build a stable quantum memory, a key component of scalable quantum computers. Traditionally, these fractional charges were observed only under large magnetic fields, but recent experiments in two-dimensional systems called moiré materials have finally found them without magnetic fields. A fundamental scientific goal is to understand how, why, and in which materials these emergent fractional charges appear. To tackle these questions, the PI and research team will develop both new computational methods and new mathematical tools. On the computational side, these systems are at the outer limit of what current techniques can handle. The PI has previously developed a specialized computational technique to study fractional charges using "tensor networks" (which are related to but distinct from neural networks). By applying this technique in tandem with other theoretical descriptions of the system, the research team will investigate questions such as whether these phenomena can be stabilized at higher temperatures and predict materials where emergence might appear. A key component of this research will be training and advancing capabilities in the quantum sciences. The PI will develop a “quantum tutorial”, a workshop on quantum computation at the University of California, San Diego, to educate the next generation quantum workforce. This tutorial will introduce quantum computing to advanced undergraduates, preparing them for research, or opening the door to industry work in the quantum sciences. Furthermore, a significant product of this work will be open-source scientific codes for studying two dimensional materials. These efforts will connect frontier research with broader educational priorities to help cultivate a quantum-aware workforce. TECHNICAL SUMMARY Moiré materials are a class of quantum materials composed of two-dimensional layers with a relative twist angle between them. By adjusting the twist angle, one can tune electronic interactions from weak to extremely strong, a regime where experiments have observed unconventional superconductors, incommensurate valley-density waves, and long-sought-after zero-field fractional quantum Hall states. The promise of such applications is hindered by the extreme difficulty of solving the many-body problem in moiré materials, as the quasi-long-range interactions and large number of fermion flavors place put them into an extremely difficult regime with intricate phase competition. The proposed research will systematically tackle the quantum many-body problem in moiré materials using both theoretical and computational approaches. The first will use the holomorphic geometry of “vortexable” or “ideal” bands to find new classes of exact ground states with topological order. Second, the research team will further develop advanced tensor network methods specifically designed for moiré materials. These complementary methods will then be applied to study the phase competition in realistic models of moiré materials, including the interplay between conventional symmetry breaking and emergent phases such as fractional quantum anomalous hall effects. A key component of this research will be training and advancing capabilities in the quantum sciences. The PI will develop a “quantum tutorial”, a workshop on quantum computation at the University of California, San Diego, to educate the next generation quantum workforce. This tutorial will introduce quantum computing to advanced undergraduates, preparing them for research, or opening the door to industry work in the quantum sciences. Furthermore, a significant product of this work will be open-source scientific codes for studying two dimensional materials. These efforts will connect frontier research with broader educational priorities to help cultivate a quantum-aware workforce. 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.