[Paper Review] Topological Duality in Floquet and Non-Hermitian Dynamical Anomalies: Extended Nielsen-Ninomiya Theorem and Chiral Magnetic Effect

Takumi Bessho, Masatoshi Sato|arXiv (Cornell University)|Jun 7, 2020

Quantum Mechanics and Non-Hermitian Physics5 citations

TL;DR

This paper extends the Nielsen-Ninomiya theorem to Floquet and non-Hermitian systems, establishing a topological duality that links bulk topological invariants directly to dynamical anomalous gapless modes. It predicts a novel non-Hermitian chiral magnetic skin effect, unifying dynamical anomalies across these systems through a duality framework.

ABSTRACT

According to conventional theory, bulk anomalous gapless states are prohibited in lattices. However, Floquet and non-Hermitian systems may dynamically realize such quantum anomalies in the bulk. Here, we present an extension of the Nielsen-Ninomiya theorem that is valid even in the presence of the bulk quantum anomaly. Particularly, the extended theorem establishes the exact correspondence between bulk topological numbers and bulk anomalous gapless modes in Floquet and non-Hermitian systems. Applying our theorem, we predict a new type of chiral magnetic effect---non-Hermitian chiral magnetic skin effect. Our work is based on the duality between Floquet and non-Hermitian systems and provides a unified understanding of the dynamical anomalies.

Motivation & Objective

• To resolve the contradiction between conventional lattice theory, which forbids bulk anomalous gapless states, and emerging Floquet and non-Hermitian systems that realize such states dynamically.
• To establish a generalized Nielsen-Ninomiya theorem valid in the presence of bulk quantum anomalies in periodically driven and non-Hermitian systems.
• To uncover a duality between Floquet and non-Hermitian systems that unifies the description of dynamical anomalies.
• To predict a new type of chiral magnetic effect—non-Hermitian chiral magnetic skin effect—arising from this duality.

Proposed method

• Develops an extended Nielsen-Ninomiya theorem that incorporates bulk topological invariants and anomalous gapless modes in Floquet and non-Hermitian systems.
• Leverages the duality between Floquet systems (periodically driven) and non-Hermitian systems (with gain-loss asymmetry) to map topological invariants across both frameworks.
• Uses topological invariants such as winding numbers and Chern numbers to classify bulk modes in the presence of dynamical anomalies.
• Applies the duality to derive the existence of chiral edge modes and skin effects in non-Hermitian systems under magnetic fields.
• Analyzes the bulk-boundary correspondence in non-Hermitian systems, showing how topological invariants directly determine the existence and chirality of anomalous modes.

Experimental results

Research questions

• RQ1 How can the Nielsen-Ninomiya theorem be generalized to include bulk quantum anomalies in Floquet and non-Hermitian systems?
• RQ2 What is the nature of the topological duality between Floquet and non-Hermitian systems in the context of dynamical anomalies?
• RQ3 Can a chiral magnetic effect emerge in non-Hermitian systems, and how does it differ from the conventional chiral magnetic effect?
• RQ4 How do topological invariants in the bulk correspond to gapless anomalous modes in these systems?

Key findings

• The extended Nielsen-Ninomiya theorem establishes an exact correspondence between bulk topological invariants and bulk anomalous gapless modes in Floquet and non-Hermitian systems.
• A new type of chiral magnetic effect—non-Hermitian chiral magnetic skin effect—is predicted, where chiral modes localize at the boundary due to non-Hermitian skin effect.
• The duality between Floquet and non-Hermitian systems enables a unified description of dynamical anomalies, revealing equivalent topological structures across both classes.
• Topological invariants such as winding numbers directly determine the existence and chirality of anomalous gapless modes in the bulk.