Topological Quantum States and the Emergence of Spatial Dimensionality

The project addresses the problem of spatial dimensionality in nature by studying phases with topological order on 3D lattices. A remarkable property of such phases is that excitations may be confined to a lower spatial dimension – although couplings exist in all directions. This study will contribute both to our knowledge of novel properties that can arise in three dimensional solids, and also serve as a laboratory to test theories of how dimensionality can be an emergent phenomenon. The main activities include: (1) developing quantum field theories of phases in 3D lattice models, displaying dimensional confinement (2) constructing and studying properties of specific lattice models with such phases, and search for physical realizations (3) exposing connections to relevant areas like high energy physics and quantum information. We expect about 6 research papers in peer reviewed journals, including 2-3 high impact publications. We expect to increase awareness of this usually neglected connection between topological order and dimensionality of space, and influence the work of a broad cross section of researchers, ranging from experimentalists searching for exotic phases in solids to high energy theorists interested in the origin of our 3 spatial dimension universe.