Fall 2020

Applying a periodic Hamiltonian to a system of particles allows us to study out-of-equilibrium matter, like the prethermal discrete time crystal (PDTC). One can define a time-independent Hamiltonian that describes the dynamics of the driven system not continuously, but in a stroboscopic manner. This implies energy conservation during the validity window of this approximation.

This talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any simply connected manifold in 2d, 3d and general dimensions. This gives a duality between all fermionic systems and a new class of 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 spacetime picture, this mapping is exactly equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action.

We develop approximations to a perturbed quantum dynamics beyond the standard approximation based on quantum Zeno dynamics and adiabatic elimination. The effective generators describing the approximate evolutions are endowed with the same block structure as the unperturbed part of the generator, and their adiabatic error is “eternal” - it does not accumulate over time. We show how this gives rise to Schrieffer-Wolff generators in open systems.