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

dc.citation.articleNumber224438en_US
dc.citation.issueNumber22en_US
dc.citation.journalTitlePhysical Review Ben_US
dc.citation.volumeNumber95en_US
dc.contributor.authorGoswami, Pallaben_US
dc.contributor.authorSi, Qimiaoen_US
dc.date.accessioned2017-09-19T18:39:59Zen_US
dc.date.available2017-09-19T18:39:59Zen_US
dc.date.issued2017en_US
dc.description.abstractIn 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 paper, 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.en_US
dc.identifier.citationGoswami, Pallab and Si, Qimiao. "Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order." <i>Physical Review B,</i> 95, no. 22 (2017) American Physical Society: https://doi.org/10.1103/PhysRevB.95.224438.en_US
dc.identifier.digitalDynamic_zero_modes_Dirac_fermionsen_US
dc.identifier.doihttps://doi.org/10.1103/PhysRevB.95.224438en_US
dc.identifier.urihttps://hdl.handle.net/1911/97404en_US
dc.language.isoengen_US
dc.publisherAmerican Physical Societyen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.titleDynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic orderen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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