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dc.contributor.authorSindelka, Milan
dc.contributor.authorSantos, Lea F.
dc.contributor.authorMoiseyev, Nimrod
dc.identifier.citationSindelka, M., Santos, L.F., and Moiseyev, N. (2017). Excited-state quantum phase transitions studied from a non-Hermitian perspective. Physical Review A 95: 010103(R).en_US
dc.description.abstractA 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 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 Padé approximants, we can extract the critical value of α.en_US
dc.description.sponsorshipM.S. was supported by the Czech Ministry of Education Grant No. LG15013, L.F.S. by the American National Science Foundation (NSF) Grants No. DMR-1147430 and No. DMR-1603418, and N.M. by the I-Core: the Israeli Excellence Center Circle of Light, by the Israel Science Foundation Grants No. 298/11 and No. 1530/15. We thank Ofir Alon, Francisco P´erez-Bernal, and Saar Rahav for fruitful discussions.en_US
dc.publisherAmerican Physical Societyen_US
dc.relation.ispartofseriesPhysical Review A;95
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.subjectquantum phase transitionsen_US
dc.subjectexceptional points (EPs)en_US
dc.subjectLipkin-Meshkov-Glick (LMG) modelen_US
dc.subjectnon-Hermitian LMG Hamiltonianen_US
dc.titleExcited-state quantum phase transitions studied from a non-Hermitian perspective.en_US

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