Geometric phase around exceptional points

Alexei Mailybaev, Oleg Kirillov, Alexander Seyranian

Research output: Contribution to journalArticlepeer-review

146 Citations (Scopus)
12 Downloads (Pure)


A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly pi for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to π for small cycles and changes as the cycle size and shape are varied. We find explicitly the leading asymptotic term of this dependence, and describe it in terms of interaction of different energy levels
Original languageEnglish
Pages (from-to)014104
JournalPhysical Review A
Issue number1
Publication statusPublished - 20 Jul 2005


Dive into the research topics of 'Geometric phase around exceptional points'. Together they form a unique fingerprint.

Cite this