Passage through exceptional point: Case study

Abstract

It is conjectured that the exceptional-point (EP) singularity of a one-parametric quasi-Hermitian $N$ by $N$ matrix Hamiltonian $H(t)$ can play the role of a quantum phase-transition interface connecting different dynamical regimes of a unitary quantum system. Six realizations of the EP-mediated quantum phase transitions "of the third kind" are described in detail. Fairly realistic Bose-Hubbard (BH) and discrete anharmonic oscillator (AO) models of any matrix dimension $N$ are considered in the initial, intermediate, or final phase. In such a linear algebraic illustration of the changes of phase, all ingredients (and, first of all, all transition matrices) are constructed in closed, algebraic, non-numerical form.

19 pages

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Light stops at exceptional points
• 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
• Conditional observability
• Three solvable matrix models of a quantum catastrophe
• Matrix Hamiltonians with an algebraic guarantee of unbroken PT-symmetry
• Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy

Cited by in corpus (11)

• Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
• Exceptional Points in the Baxter-Fendley Free Parafermion Model
• A Brief History of Free Parafermions
• Paths of unitary access to exceptional points
• Unitary unfoldings of Bose-Hubbard exceptional point with and without particle number conservation
• Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• Exceptional point rings and $PT$-symmetry in the non-Hermitian XY model
• Construction of maximally non-Hermitian potentials under unbroken PT-symmetry constraint
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians
• Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model