Exceptional spectrum and dynamic magnetization

TL;DR

This paper introduces a family of non-Hermitian many-body systems exhibiting exceptional spectra and demonstrates how complex fields can induce macroscopic magnetization dynamics, including reversing ferromagnetic states, with universal behavior across various conditions.

Contribution

It proposes a new class of non-Hermitian systems with all eigenstates coalescing, leading to unique macroscopic phenomena and dynamic magnetization driven by complex fields.

Findings

All single-particle eigenstates coalesce with a single unidirectional coupling.

Dynamic magnetization can reverse ferromagnetic states using complex fields.

Magnetization dynamics show universal behavior across different system configurations.

Abstract

A macroscopic effect can be induced by a local non-Hermitian term in a many-body system, when it manifests simultaneously level coalescence of a full real degeneracy spectrum, leading to exceptional spectrum. In this paper, we propose a family of systems that support such an intriguing property. It is generally consisted of two arbitrary identical Hermitian sub-lattices in association with unidirectional couplings between them. We show exactly that all single-particle eigenstates coalesce in pairs even only single unidirectional coupling appears. It means that all possible initial states obey the exceptional dynamics, resulting in some macroscopic phenomena, which never appears in a Hermitian system. As an application, we study the dynamic magnetization induced by complex fields in an itinerant electron system. It shows that an initial saturated ferromagnetic state at half-filling can be driven into its opposite state according to the dynamics of high-order exceptional point. Any Hermitian quench term cannot realize a steady opposite saturated ferromagnetic state. Numerical simulations for the dynamical processes of magnetization are performed for several representative situations, including lattice dimensions, global random and local impurity distributions. It shows that the dynamic magnetization processes exhibit universal behavior.