Non-Hermitian dynamics of a two-spin system with PT symmetry

TL;DR

This paper explores the complex dynamics of a two-spin system under PT-symmetric non-Hermitian conditions, revealing exceptional points, bistability, and stable oscillations with geometric insights.

Contribution

It introduces a detailed analysis of nonlinear two-spin PT-symmetric systems, identifying conserved quantities and providing a geometric framework for their dynamics.

Findings

Identification of an exceptional point in nonlinear PT-symmetric spin systems

Bistability and stable oscillations in the nonlinear regime

Derivation of conserved quantities for spin trajectories

Abstract

A system of interacting spins that are under the influence of spin-polarized currents can be described using a complex functional, or a non-Hermitian (NH) Hamiltonian. We study the dynamics of two exchange-coupled spins on the Bloch sphere. In the case of currents leading to PT symmetry, an exceptional point that survives also in the nonlinear system is identified. The nonlinear system is bistable for small currents and it exhibits stable oscillating motion or it can relax to a fixed point. The oscillating motion of the two spins is akin to synchronized spin-torque oscillators. For the full nonlinear system, we derive two conserved quantities that furnish a geometric description of the spin trajectories in phase space and indicate stability of the oscillating motion. Our analytical results provide tools for the description of the dynamics of NH systems that are defined on the Bloch sphere.