Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order

TL;DR

This paper develops a theoretical framework to understand how Dirac fermions coupled with antiferromagnetic order can give rise to competing singlet phases, especially near quantum phase transitions, using topological and fermionic zero mode analysis.

Contribution

It introduces a topological mechanism involving fermion zero modes to analyze competing singlet orders in itinerant Dirac fermion systems near magnetic quantum critical points.

Findings

Fermion zero modes suppress tunneling events in hedgehog configurations.

The nature of emergent singlet order depends on zero mode overlaps between hedgehogs and antihedgehogs.

Demonstrates competition between spin Peierls order and Kondo singlet formation in a honeycomb lattice model.

Abstract

In quantum spin systems, singlet phases often develop in the vicinity of an antiferromagnetic order. Typical settings for such problems arise when itinerant fermions are also present. In this work, we develop a theoretical framework for addressing such competing orders in an itinerant system, described by Dirac fermions strongly coupled to an O(3) nonlinear sigma model. We focus on two spatial dimensions, where upon disordering the antiferromagnetic order by quantum fluctuations the singular tunneling events also known as (anti)hedgehogs can nucleate competing singlet orders in the paramagnetic phase. In the presence of an isolated hedgehog configuration of the nonlinear sigma model field, we show that the fermion determinant vanishes as the dynamic Euclidean Dirac operator supports fermion zero modes of definite chirality. This provides a topological mechanism for suppressing the tunneling events. Using the methodology of quantum chromodynamics, we evaluate the fermion determinant in the close proximity of magnetic quantum phase transition, when the antiferromagnetic order parameter field can be described by a dilute gas of hedgehogs and antihedgehogs. We show how the precise nature of emergent singlet order is determined by the overlap between dynamic fermion zero modes of opposite chirality, localized on the hedgehogs and antihedgehogs. For a Kondo-Heisenberg model on the honeycomb lattice, we demonstrate the competition between spin Peierls order and Kondo singlet formation, thereby elucidating its global phase diagram. We also discuss other physical problems that can be addressed within this general framework.