Realizing 2D topologically ordered states and their phase transitions in a programmable quantum processor.
Abstract: The search for exotic quantum phases of matter is a central theme in condensed matter physics. The advent of programmable quantum hardware provides an unprecedented access to novel quantum states and represents a new avenue for probing the exotic properties associated with topological order.. In this talk, I will discuss our progress in realization of topologically ordered ground states based on exact efficient quantum circuit representations.
Exact bosonization in all dimensions and the duality between fermionic SPT and higher-group bosonic SPT phases
The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any manifold in 2d, 3d, and general dimensions. This gives a duality between all fermionic systems and a new class of Z2 lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action.
Beyond Topological Order: Fractons and Their Field Theory
Recently, exactly solvable 3D lattice models have been discovered for a new kind of phase, dubbed fracton topological order, in which the topological excitations are immobile or are bound to lines or surfaces. Unlike liquid topologically ordered phases (e.g. Z_2 gauge theory), which are only sensitive to topology (e.g. the ground state degeneracy only depends on the topology of spatial manifold), fracton orders are also sensitive to the geometry of the lattice.