Quantum phase transitions mediated by clustered non-Hermitian degeneracies

• URL: http://arxiv.org/abs/2102.12272v1
• Date: Wed, 24 Feb 2021 13:17:55 GMT
• Title: Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Authors: Miloslav Znojil
• Abstract summary: A family of phase transitions in closed and open quantum systems is known to be mediated by a non-Hermitian degeneracy. In our paper the EP-mediated quantum phase transitions with $K>1$ are called "clustered" For the sake of maximal simplicity our attention is restricted to the real-harmonic-oscillator-type N by N matrix Hamiltonians.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A broad family of phase transitions in the closed as well as open quantum systems is known to be mediated by a non-Hermitian degeneracy (a.k.a. exceptional point, EP) of the Hamiltonian. In the EP limit, in general, the merger of an $N-$plet of the energy eigenvalues is accompanied by a parallel (though not necessarily complete) degeneracy of eigenstates (forming an EP-asociated $K-$plet; in mathematics, $K$ is called the geometric multiplicity of the EP). In the literature, unfortunately, only the benchmark matrix models with $K=1$ can be found. In our paper the gap is filled: the EP-mediated quantum phase transitions with $K>1$ are called "clustered", and a family of benchmark models admitting such a clustering phenomenon is proposed and described. For the sake of maximal simplicity our attention is restricted to the real perturbed-harmonic-oscillator-type N by N matrix Hamiltonians which are exactly solvable and in which the perturbation is multiparametric (i.e., maximally variable) and antisymmetric (i.e., maximally non-Hermitian). A labeling (i.e., an exhaustive classification) of these models is provided by a specific partitioning of N.

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