Microscopic Theories of Quantum Matter

Washington University, Saint Louis MO

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports research and education on fundamental organization principles of matter with the innate capacity for the technological harvesting of quantum physics. Matter displays the remarkable tendency to organize itself into different phases, such as liquid, gas, or solid. At the microscopic level, different phases of matter correspond to different organization principles, also known as orders. For some states of matter, these orders favor the emergence of entirely new particles that cannot exist in vacuum, but are prisoners to their phase of matter, and can have spectacular and useful properties. One class of such emergent new particles is known as “anyons”. These particles exhibit the “spooky action at a distance”, which Einstein attributed to quantum phenomena in a most dramatic way. Concretely, this means that they open up revolutionary avenues for information processing, causing exponential speed-up for certain calculations when compared to classical computers, while being more robust compared to other schemes of quantum computing. This project will address a central dilemma accompanying the exciting prospect of anyon physics: There exist a wealth of theoretical models predicting the existence of anyons with great clarity, and there exist experimental platforms where certain types of anyons are widely expected to exist. However, most models do not allow for practical realization, and existing experimental systems make characterization and direct control of anyons highly challenging. The project team will harvest and further develop recent theoretical progress to make contact with present-day capabilities for building artificial materials. Theoretical models will be developed that are now within grasp of these capabilities and will give access to a rich world of anyon physics in the presence of unprecedented experimental control. The same approach will be extended to other forms of matter and collective quantum phenomena that have only recently come within the reach of our experimental capacities, such as the so-called supersolids. The project will further develop the interface between condensed matter physics and other areas of physics, such as quantum information, as well as pure mathematics, and pave the way for technological applications hinging on this interface. The project will train graduate students in the PI’s group, which have included women and/or underrepresented minorities in STEM, and offer mentored research experiences for undergraduate students. Result will be communicated to the public via Washington University’s public lecture series and outreach activities sponsored by the Center for Quantum Sensors. TECHNICAL SUMMARY This award supports research and education on the fundamental understanding of correlated matter. The ability to gain insight into universal properties of interacting quantum many-body systems hinges on the realization that certain forms of order prevail over all complexity. Among the most fascinating orders known are topological orders, realized in fractional quantum Hall liquids and suspected to be possible in quantum magnets and cold atom systems. Emergent phenomena in these systems are inherently quantum in nature, lending an unusual stability to macroscopic superpositions and making them nearly ideal for certain schemes of quantum computing. The knowledge that these and other intricate states of matter in principle exist comes with the challenge of defining conditions that stabilize them. Experimental conditions, where, specifically, topological orders are widely accepted to exist, so far afford too limited control to probe their most defining features directly. On the other hand, a new era of quantum control is dawning, where on certain platforms, Hamiltonians of unprecedented complexity can be engineered. It nonetheless remains challenging to construct Hamiltonians with guaranteed ground state properties, especially for non-Abelian phases, that are within reach of these new quantum technologies. The project will break new ground on these and related problems via: (i) Construction of a class of lattice Hamiltonians with highly local two-body interactions (as opposed to "more than two"-body) whose ground state properties are exactly known, and are those defining a non-Abelian topological phase, (ii) Construction of local lattice models with exactly known quantum many-body-scars of exactly computable bipartite entanglement entropy in a quantum dimer setting, whose Hilbert space size scaling is very favorable for complementary exact diagonalization, (iii) Extension of Pfaffian methods for dimer models, a traditional powerhouse for creating solvable models in quantum many-body and statistical physics, to certain non-planar lattice graphs, and (iv) Further development of a coupled-chain approach to explain the existence and stability of some phases of exotic matter. The project will further develop the interface between condensed matter physics and other areas of physics, such as quantum information, as well as pure mathematics, and pave the way for technological applications hinging on this interface. The project will train graduate students in the PI’s group, which have included women and/or underrepresented minorities in STEM, and offer mentored research experiences for undergraduate students. Result will be communicated to the public via Washington University’s public lecture series and outreach activities sponsored by the Center for Quantum Sensors. 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.