Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator

Abstract

Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases.

v1: Comments are welcome; v2: This version contains some new calculations and corrects some errors from the older version; v3: Substantially revised and to appear in Physica Scripta

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Cited by in corpus (5)

• Quantum entanglement and non-Hermiticity in free-fermion systems
• Enhanced frequency and temperature estimation by a $\mathcal{P}\mathcal{T}$-symmetric quantum oscillator
• Phase transitions in quasi-Hermitian quantum models at exceptional points of order four
• Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics