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Related papers: Kitaev model in regular hyperbolic tilings

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We study the quantum phase transition between Abelian and non-Abelian phases in an extended Kitaev spin model on the honeycomb lattice, where the periodic boundary condition is applied by placing the lattice on a torus. Our analytical…

Statistical Mechanics · Physics 2015-05-13 Xiao-Feng Shi , Yue Yu , J. Q. You , Franco Nori

The Kitaev model is an exactly solvable quantum spin model within the language of the constrained real fermions. In spite of numerous studies along special magnetic-field orientations, there is a limited amount of knowledge on the complete…

Strongly Correlated Electrons · Physics 2022-02-15 F. Yılmaz , A. P. Kampf , S. K. Yip

Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum computation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we…

Quantum Physics · Physics 2012-09-10 Ze-Liang Xiang , Ting Yu , Wenxian Zhang , Xuedong Hu , J. Q. You

The $S=1/2$ Kitaev honeycomb model has attracted significant attention as an exactly solvable example with a quantum spin liquid ground state. In a properly oriented external magnetic field, chiral Majorana edge modes associated with a…

Strongly Correlated Electrons · Physics 2022-03-23 Pedro M. Cônsoli , Eric C. Andrade

The hexagonal tiling honeycomb is a beautiful structure in 3-dimensional hyperbolic space. It is called {6,3,3} because each hexagon has 6 edges, 3 hexagons meet at each vertex in a Euclidean plane tiled by regular hexagons, and 3 such…

History and Overview · Mathematics 2024-12-03 John C. Baez

Kitaev's honeycomb model is a paradigmatic exactly solvable system hosting a quantum spin liquid with non-Abelian anyons and topologically protected edge modes, offering a platform for fault-tolerant quantum computation. However, real…

Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive…

Computational Physics · Physics 2025-08-08 Yanick Thurn , Manuel Schrauth , Johanna Erdmenger

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented…

Strongly Correlated Electrons · Physics 2017-02-01 Dorota Gotfryd , Juraj Rusnačko , Krzysztof Wohlfeld , George Jackeli , Jiří Chaloupka , Andrzej M. Oleś

The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological $\mathbb{Z}_2$ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic…

Strongly Correlated Electrons · Physics 2026-05-04 Will Holdhusen , Daniel Huerga , Gerardo Ortiz

We investigate a bilayer Kitaev model, where two honeycomb layers are coupled by the Heisenberg interactions, to discuss effects of an interlayer coupling against the Kitaev quantum spin liquids (QSLs). In this model, there exists a local…

Strongly Correlated Electrons · Physics 2018-03-06 Hiroyuki Tomishige , Joji Nasu , Akihisa Koga

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev…

Mesoscale and Nanoscale Physics · Physics 2024-06-19 Tessa Cookmeyer , Sankar Das Sarma

The ruby lattice is a four-valent lattice interpolating between honeycomb and triangular lattices. In this work we investigate the topological spin-liquid phases of a spin Hamiltonian with Kitaev interactions on the ruby lattice using exact…

Strongly Correlated Electrons · Physics 2016-09-28 Saeed S. Jahromi , Mehdi Kargarian , S. Farhad Masoudi , Abdollah Langari

We report the existence of \emph{flat bands} in a p-wave superconducting Kitaev ladder. We identify two sets of parameters for which the Kitaev ladder sustains flat bands. These flat bands are accompanied by highly localized eigenstates…

Mesoscale and Nanoscale Physics · Physics 2020-02-24 Ritu Nehra , Devendra Singh Bhakuni , Ajith Ramachandran , Auditya Sharma

We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…

Mesoscale and Nanoscale Physics · Physics 2009-07-22 F. A. Bais , J. K. Slingerland , S. M. Haaker

We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two…

Geometric Topology · Mathematics 2019-04-09 Benedikt Kolbe , Vanessa Robins

An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice which exhibits both Abelian and non-Abelian phases, the model has two…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Shinsei Ryu

We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained…

Statistical Mechanics · Physics 2009-12-10 François Sausset , Cristina Toninelli , Giulio Biroli , Gilles Tarjus

Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Using Monte Carlo simulations…

Strongly Correlated Electrons · Physics 2025-12-10 Ivan Dutta , Anamitra Mukherjee , Onur Erten , Kush Saha

We study the excitations in a three dimensional version of Kitaev's spin-1/2 model on the honeycomb lattice introduced by the present authors recently. The gapped phase of the system is analyzed using a low energy effective Hamiltonian…

Strongly Correlated Electrons · Physics 2014-12-03 Saptarshi Mandal , Naveen Surendran

The honeycomb lattice Kitaev model H_{K} with two kinds of Wen-Toric-code four-body interactions H_{WT} is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body…

Statistical Mechanics · Physics 2019-02-20 Kazuhiko Minami