Non-Hermitian tight-binding network engineering

TL;DR

This paper introduces a straightforward approach to engineer non-Hermitian tight-binding quantum networks using auxiliary clusters, enabling complex hopping rates with only complex on-site energies, demonstrated through three applications.

Contribution

It presents a novel method for Hamiltonian engineering in quantum networks by coupling to non-Hermitian clusters, expanding control over complex hopping dynamics.

Findings

Realized effective complex non-Hermitian hopping with only complex on-site energies.

Engineered a nearly transparent defect in a Hermitian lattice.

Synthesized a PT-symmetric lattice with a bound state in the continuum.

Abstract

We suggest a simple method to engineer a tight-binding quantum network based on proper coupling to an auxiliary non-Hermitian cluster. In particular, it is shown that effective complex non-Hermitian hopping rates can be realized with only complex on-site energies in the network. Three applications of the Hamiltonian engineering method are presented: the synthesis of a nearly transparent defect in an Hermitian linear lattice; the realization of the Fano-Anderson model with complex coupling; and the synthesis of a $\mathcal{PT}$-symmetric tight-binding lattice with a bound state in the continuum.