Exotic quantum holonomy and non-Hermitian degeneracies in the two-body Lieb–Liniger model

Abstract

An interplay of an exotic quantum holonomy and exceptional points is examined in onedimensional Bose systems. The eigenenergy anholonomy, in which Hermitian adiabatic cycle induces nontrivial change in eigenenergies, can be interpreted as a manifestation of eigenenergy's Riemann surface structure, where the branch points are identified as the exceptional points which are degeneracy points in the complexified parameter space. It is also shown that the exceptional points are the divergent points of the non-Abelian gauge connection for the gauge theoretical formulation of the eigenspace anholonomy. This helps us to evaluate anti-path-ordered exponentials of the gauge connection to obtain gauge covariant quantities.

Bloch vector, disclination and exotic quantum holonomy

“…The adiabatic time evolution under the presence of the eigenspace anholonomy resembles a parametric evolution that encloses an EP, in the sense that these evolutions permutate eigenspaces. An analytic continuation of adiabatic cycle in Hermitian Hamiltonian and unitary Floquet systems has enabled to interpret the exotic quantum holonomy as the result of parametric encirclement of EP in the complex plane [30,31]. Although such a correspondence is valid only when an analytic continuation of the adiabatic cycle is available, the topological formulation is applicable regardless of the analytic continuation.…”

“…Secondly, Viennot proposed another gauge theoretical formulation based on the adiabatic Floquet theory, where the nontrivial Floquet block change is discussed in terms of gerbes [29]. Thirdly, the exotic quantum holonomy is associated to the state flip induced by EPs through the generalized Fujikawa formalism [30,31]. Here the analytic continuation of a Hermitian (or unitary) adiabatic cycle provides non-Hermitian cycles, which relate the Riemann surface structure of eigenenergies [32] to the exotic quantum holonomy.…”

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

“…[25,26] by using a 3 × 3 nonHermitian matrix. The exotic quantum holonomy associated with multiple EPs is also studied in the two-body Lieb-Liniger model [27]. However, the multiply degenerated EP has been rarely investigated (see Ref.…”