Exotic quantum holonomy and its topological formulation

A quasi-static adiabatic cycle may induce a nontrivial change on the phase of a stationary state of a closed quantum system. This is known as the phase holonomy or the geometric phase. It has been recognized that eigenspaces also exhibit nontrivial change due to adiabatic cycles. This is referred to as an exotic quantum holonomy (EQH). Examples of EQH has been found in a one-dimensional particle subject to the generalized point interaction, a quantum map under a rank-1 perturbation, one-dimensional Bose systems (the Lieb-Liniger model), quantum graphs and so on. After the introduction of (some of) these examples, I will explain a topological formulation for EQH, which is a counterpart of Simon's fiber formulation for the geometric phase. In our formulation, the EQH in two-level systems is interpreted as the disclination, a kind of topological defects, of the director (headless vector) related with the "Bloch vector".

Ref. A. Tanaka and T. Cheon, Physics Letters A379, 1693 (2015).

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