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Phys. Rev. E 78, 015202(R) (2008) [4 pages]

Geometric phases and quantum phase transitions in open systems

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Alexander I. Nesterov*
Departamento de Física, CUCEI, Universidad de Guadalajara, Av. Revolución 1500, Guadalajara, Codigo Postal 44420, Jalisco, México

S. G. Ovchinnikov†
L. V. Kirensky Institute of Physics, SB RAS, 660036, Krasnoyarsk, Russia and Siberian Federal University, 660041, Krasnoyarsk, Russia

Received 13 November 2007; revised 18 April 2008; published 18 July 2008

The relationship is established between quantum phase transitions and complex geometric phases for open quantum systems governed by a non-Hermitian effective Hamiltonian with accidental crossing of the eigenvalues. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that the related quantum phase transition is of the first order.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.78.015202
DOI:
10.1103/PhysRevE.78.015202
PACS:
03.65.Vf, 14.80.Hv, 03.65.−w, 03.67.−a

*nesterov@cencar.udg.mx

†sgo@iph.krasn.ru

 
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