Exotic quantum holonomy and non-Hermitian degeneracies in two-body Lieb-Liniger model
arXiv:1305.1693 · doi:10.1088/1751-8113/46/31/315302
Abstract
An interplay of an exotic quantum holonomy and exceptional points is examined in one-dimensional 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.
12 pages, 4 figures
References in corpus (5)
- Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
- Lieb-Liniger model of a dissipation-induced Tonks-Girardeau gas
- Quasienergy anholonomy and its application to adiabatic quantum state manipulation
- Quantum holonomy in Lieb-Liniger model
- Gauge invariants of eigenspace and eigenvalue anholonomies: Examples in hierarchical quantum circuits