Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field

The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid-state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type o...

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Autores principales:	Erik S. Sørensen, Andrei Catuneanu, Jacob S. Gordon, Hae-Young Kee
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/4d56d6264eb64c639aac19dd13d99f54
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spelling	oai:doaj.org-article:4d56d6264eb64c639aac19dd13d99f542021-12-02T14:26:20ZHeart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field10.1103/PhysRevX.11.0110132160-3308https://doaj.org/article/4d56d6264eb64c639aac19dd13d99f542021-01-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.011013http://doi.org/10.1103/PhysRevX.11.011013https://doaj.org/toc/2160-3308The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid-state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type of bond-dependent term, has been particularly challenging to fully understand. A minimal Kitaev-Gamma model has been investigated by various numerical techniques under a magnetic field, but definite conclusions about field-induced spin liquids remain elusive. One reason for this may lie in the limited sizes of the two-dimensional geometry it is possible to access numerically, and missed incommensurately ordered states may be interpreted as a spin liquid. Here we focus on the Kitaev-Gamma ladder model as a guide to the phase space of disordered states which could potentially become a spin liquid in the two-dimensional limit. We determine the entire phase diagram in the presence of a magnetic field along the [111] direction. Because of the competition between the interactions and the field, an extremely rich phase diagram emerges with 15 distinct phases. Focusing near the antiferromagnetic Kitaev region, we identify nine different phases solely within this region: several incommensurate magnetically ordered phases, spin-nematic, and two chiral phases with enhanced entanglement. Of particular interest is a highly entangled phase with staggered chirality with zero-net flux occurring at intermediate field, which along with its companion phases outlines a heart-shaped region of high entanglement, the heart of entanglement. We compare our results for the ladder with a C_{3} symmetric cluster of the two-dimensional honeycomb lattice, and offer insight into possible spin liquids in the two-dimensional limit.Erik S. SørensenAndrei CatuneanuJacob S. GordonHae-Young KeeAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 1, p 011013 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Erik S. Sørensen Andrei Catuneanu Jacob S. Gordon Hae-Young Kee Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
description	The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid-state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type of bond-dependent term, has been particularly challenging to fully understand. A minimal Kitaev-Gamma model has been investigated by various numerical techniques under a magnetic field, but definite conclusions about field-induced spin liquids remain elusive. One reason for this may lie in the limited sizes of the two-dimensional geometry it is possible to access numerically, and missed incommensurately ordered states may be interpreted as a spin liquid. Here we focus on the Kitaev-Gamma ladder model as a guide to the phase space of disordered states which could potentially become a spin liquid in the two-dimensional limit. We determine the entire phase diagram in the presence of a magnetic field along the [111] direction. Because of the competition between the interactions and the field, an extremely rich phase diagram emerges with 15 distinct phases. Focusing near the antiferromagnetic Kitaev region, we identify nine different phases solely within this region: several incommensurate magnetically ordered phases, spin-nematic, and two chiral phases with enhanced entanglement. Of particular interest is a highly entangled phase with staggered chirality with zero-net flux occurring at intermediate field, which along with its companion phases outlines a heart-shaped region of high entanglement, the heart of entanglement. We compare our results for the ladder with a C_{3} symmetric cluster of the two-dimensional honeycomb lattice, and offer insight into possible spin liquids in the two-dimensional limit.
format	article
author	Erik S. Sørensen Andrei Catuneanu Jacob S. Gordon Hae-Young Kee
author_facet	Erik S. Sørensen Andrei Catuneanu Jacob S. Gordon Hae-Young Kee
author_sort	Erik S. Sørensen
title	Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
title_short	Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
title_full	Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
title_fullStr	Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
title_full_unstemmed	Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
title_sort	heart of entanglement: chiral, nematic, and incommensurate phases in the kitaev-gamma ladder in a field
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/4d56d6264eb64c639aac19dd13d99f54
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Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field

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