Type: Article
Publication Date: 2009-10-26
Citations: 42
DOI: https://doi.org/10.1088/1751-8113/42/46/465211
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 -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 -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 turn out to be unique with the sole assumption that the Dyson map is Hermitian. Finally, we analyse the magnetization of the chain in the z- and x-direction.