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

0487461 - FZÚ 2018 RIV 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), s. 1-5, č. článku 010103. ISSN 2469-9926. E-ISSN 2469-9934
R&D Projects: GA MŠMT LG15013
Institutional support: RVO:68378271
Keywords : exceptional points * systems * model * signatures * dynamics * freedom * spectra
OECD category: Fluids and plasma physics (including surface physics)
Impact factor: 2.909, year: 2017

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. 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 α that lead to the EPs approach the real axis as the system size N →∞. 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 Pad´e approximants, we can extract the critical value of α.

Permanent Link: http://hdl.handle.net/11104/0282117