PT symmetric lattices with a local degree of freedom

TL;DR

This paper explores how a local pseudospin degree of freedom influences the behavior of a one-dimensional $ ext{PT}$-symmetric lattice, revealing conditions for decoupling and tunable symmetry-breaking thresholds.

Contribution

It introduces a model incorporating a local pseudospin into a $ ext{PT}$-symmetric lattice and demonstrates how symmetry under pseudospin exchange leads to decoupled subsystems with adjustable $ ext{PT}$-symmetry breaking thresholds.

Findings

Decoupling of the system into two independent parts under pseudospin exchange symmetry

Tunable threshold for $ ext{PT}$ symmetry breaking in each subsystem

Implications for specific tunneling profiles and boundary conditions

Abstract

Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{PT}$) operations. Here, we model and investigate the effects of a local, two-state, quantum degree of freedom, called a pseudospin, on a one-dimensional tight-binding lattice with position-dependent tunneling amplitudes and a single pair of non-Hermitian, $\mathcal{PT}$-symmetric impurities. We show that if the resulting Hamiltonian is invariant under exchange of two pseudospin labels, the system can be decomposed into two uncoupled systems with tunable threshold for $\mathcal{PT}$ symmetry breaking. We discuss implications of our results to systems with specific tunneling profiles, and open or periodic boundary conditions.