Excited-state quantum phase transitions studied from a non-Hermitian perspective

0494834 - ÚFP 2019 US eng J - Journal Article
Šindelka, Milan - Santos, L.F. - Moiseyev, N.
Excited-state quantum phase transitions studied from a non-Hermitian perspective.
Physical Review A. Roč. 95, č. 1 (2017), č. článku 010103. ISSN 2469-9926. E-ISSN 2469-9934
R&D Projects: GA MŠMT LG15013
Institutional support: RVO:61389021
Keywords : Excited states * Hamiltonians * Phase transitions
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.909, year: 2017
https://link.aps.org/accepted/10.1103/PhysRevA.95.010103

A main distinguishing feature of non-Hermitian quantum mechanics is the presence of exceptional points (EPs). They correspond to the coalescence of two energy levels and their respective eigenvectors. Here, we use the Lipkin-Meshkov-Glick (LMG) model as a test bed to explore the strong connection between EPs and the onset of excited state quantum phase transitions (ESQPTs). We show that for finite systems, the exact degeneracies (EPs) obtained with the non-Hermitian LMG Hamiltonian continued into the complex plane are directly linked with the avoided crossings that characterize the ESQPTs for the real (physical) LMG Hamiltonian. The values of the complex control parameter alpha that lead to the EPs approach the real axis as the system size N -> infinity. This happens for both the EPs that are close to the separatrix that marks the ESQPT and also for those that are far away, although in the latter case, the convergence rate is smaller. With the method of Pade approximants, we can extract the critical value of alpha.
Permanent Link: http://hdl.handle.net/11104/0287895