Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops

Abstract

The correspondence between exotic quantum holonomy, which occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expression of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, is obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher-order EP, which is broken into lower-order EPs with the application of small perturbations. The stability of exotic holonomy against such bifurcation is demonstrated.

Floquet semimetal with Floquet-band holonomy

“…That is, eigenstates of U (λ) may have made transitions even though U (λ) itself has returned. This remarkable phenomenon (much different from Berry phase or Wilczek-Zee phase) is still under investigation [35][36][37] . How such Floquet holonomy may lead to novel FTPs is the main motivation of this paper.…”

Multiply Degenerate Exceptional Points and Quantum Phase Transitions

“…In a suitable basis they acquire a Jordan-blocks-containing canonical form [1,5,6]. Thus, even if one of values of λ (EP ) j is real, the limiting transition λ → λ (EP ) j must still be perceived as a process during which certain eigenvectors of H (λ) "parallelize" and become linearly dependent, resulting in the loss of the usual probabilistic tractability of the quantum system in question [7][8][9][10][11][12][13].…”