Quantum phase transitions mediated by clustered non-Hermitian degeneracies
arXiv:2102.12272 · doi:10.1103/PhysRevE.103.032120
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 plet of the energy eigenvalues is accompanied by a parallel (though not necessarily complete) degeneracy of eigenstates (forming an EP-asociated plet; in mathematics, is called the geometric multiplicity of the EP). In the literature, unfortunately, only the benchmark matrix models with can be found. In our paper the gap is filled: the EP-mediated quantum phase transitions with 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.
arXiv comment26 pages, supersedes unpublished arXiv:2010.15014
References in corpus (37)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- Complex Extension of Quantum Mechanics
- The physics of exceptional points
- Pseudo-Hermitian Representation of Quantum Mechanics
- Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
- Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
- The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
- Supersymmetry and the spontaneous breakdown of PT symmetry
- Light stops at exceptional points
- High-order exceptional points in optomechanics
- Coalescence of spectral singularities and phase diagrams for one-dimensional PT symmetric photonic crystals
- Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators
- Robust and fragile PT-symmetric phases in a tight-binding chain
- Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
- Operator (quasi-)similarity, quasi-Hermitian operators and all that
- Three-Hilbert-Space Formulation of Quantum Mechanics
- Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
- Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
- Conserved quantities in parity-time symmetric systems
- Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
- Non-self-adjoint hamiltonians defined by Riesz bases
- Quantum catastrophes: a case study
- Unitarity corridors to exceptional points
- Admissible perturbations and false instabilities in PT-symmetric quantum systems
- Three solvable matrix models of a quantum catastrophe
- Quantum phase transitions in nonhermitian harmonic oscillator
- Passage through exceptional point: Case study
- Complex symmetric Hamiltonians and exceptional points of order four and five
- Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
- Quantum inner-product metrics via recurrent solution of Dieudonne equation
- Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy
- Perturbation theory near degenerate exceptional points
- Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
- Anomalous mechanisms of the loss of observability in non-Hermitian quantum models
- Hermitian--to--quasi-Hermitian quantum phase transitions
- Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation