City Research Online

Abstract

We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turns out to be unique with the sole assumption that the Dyson map is Hermitian. Finally we compute the magnetization of the chain in the z and x direction.

Publication Type:	Article
Publisher Keywords:	LEE EDGE SINGULARITY, PT-SYMMETRY, HAMILTONIANS, FERROMAGNET, OSCILLATOR, OPERATORS, XXZ
Subjects:	Q Science > QC Physics
Departments:	School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

Export

Downloads