Exotic quantum holonomy induced by degeneracy hidden in complex parameter space

Sang Wook Kim; Taksu Cheon; Atushi Tanaka

doi:10.1016/j.physleta.2010.02.058

Exotic quantum holonomy induced by degeneracy hidden in complex parameter space

Sang Wook Kim
, Taksu Cheon
, Atushi Tanaka

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

An adiabatic change of a bound state along a closed circuit in the parameter space can induce holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial characteristics of the exotic holonomies.

Original language	English
Pages (from-to)	1958-1961
Number of pages	4
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	374
Issue number	19-20
DOIs	https://doi.org/10.1016/j.physleta.2010.02.058
Publication status	Published - 19 Apr 2010

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Nos. 2009-0084606 and 2009-0087261 ), and also by the Grant-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science and Technology, Japan (Grant numbers 18540384 and 21540402 ).

Keywords

Exceptional point
Geometric phase
Non-Abelian holonomy

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10.1016/j.physleta.2010.02.058

Cite this

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title = "Exotic quantum holonomy induced by degeneracy hidden in complex parameter space",

abstract = "An adiabatic change of a bound state along a closed circuit in the parameter space can induce holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial characteristics of the exotic holonomies.",

keywords = "Exceptional point, Geometric phase, Non-Abelian holonomy",

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note = "Funding Information: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Nos. 2009-0084606 and 2009-0087261 ), and also by the Grant-in-Aid for Scientific Research of Ministry of Education, Culture, Sports, Science and Technology, Japan (Grant numbers 18540384 and 21540402 ).",

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AU - Cheon, Taksu

AU - Tanaka, Atushi

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PY - 2010/4/19

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N2 - An adiabatic change of a bound state along a closed circuit in the parameter space can induce holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial characteristics of the exotic holonomies.

AB - An adiabatic change of a bound state along a closed circuit in the parameter space can induce holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial characteristics of the exotic holonomies.

KW - Exceptional point

KW - Geometric phase

KW - Non-Abelian holonomy

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DO - 10.1016/j.physleta.2010.02.058

M3 - Article

AN - SCOPUS:77949918981

SN - 0375-9601

VL - 374

SP - 1958

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 19-20

ER -

Exotic quantum holonomy induced by degeneracy hidden in complex parameter space

Abstract

Bibliographical note

Keywords

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