Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands
Fractional excitations hold immense promise for both fundamental physics and quantum technologies. However, constructing lattice models for their dynamics under gauge fields remains a formidable challenge due to inherent obstructions. Here, we introduce a novel and systematic framework for deriving...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-07-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/37kh-kc81 |
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| author | K. B. Yogendra G. Baskaran Tanmoy Das |
| author_facet | K. B. Yogendra G. Baskaran Tanmoy Das |
| author_sort | K. B. Yogendra |
| collection | DOAJ |
| description | Fractional excitations hold immense promise for both fundamental physics and quantum technologies. However, constructing lattice models for their dynamics under gauge fields remains a formidable challenge due to inherent obstructions. Here, we introduce a novel and systematic framework for deriving low-energy lattice models of fractional orbitals coupled to tight-binding gauge fields. Departing from conventional geometric approaches, our method systematically eliminates the high-energy states via virtual hopping, thereby deriving the gauge potential and quantum metric through a superexchange mechanism. We demonstrate the framework by constructing Wannier orbitals for Majorana states and a tight-binding Z_{2} gauge field across various flux-crystalline phases in the Kitaev spin model on a honeycomb lattice. Our study reveals a striking phase transition between two nontrivial topological phases characterized by gapless flat band with extensive degeneracy. Furthermore, we develop a gauge-invariant mean-field theory for interacting Majorana orbitals, leading to a fractional Chern state. Our work establishes a general framework for gauge-mediated tight-binding models and a gauge-invariant mean-field theory for interacting fractional orbitals that can be readily extended to U(1), SU(N) lattice gauge theories. |
| format | Article |
| id | doaj-art-bef2135cf80e406b8a9ad920cdeea052 |
| institution | Kabale University |
| issn | 2160-3308 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj-art-bef2135cf80e406b8a9ad920cdeea0522025-08-20T03:51:00ZengAmerican Physical SocietyPhysical Review X2160-33082025-07-0115303102010.1103/37kh-kc81Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana BandsK. B. YogendraG. BaskaranTanmoy DasFractional excitations hold immense promise for both fundamental physics and quantum technologies. However, constructing lattice models for their dynamics under gauge fields remains a formidable challenge due to inherent obstructions. Here, we introduce a novel and systematic framework for deriving low-energy lattice models of fractional orbitals coupled to tight-binding gauge fields. Departing from conventional geometric approaches, our method systematically eliminates the high-energy states via virtual hopping, thereby deriving the gauge potential and quantum metric through a superexchange mechanism. We demonstrate the framework by constructing Wannier orbitals for Majorana states and a tight-binding Z_{2} gauge field across various flux-crystalline phases in the Kitaev spin model on a honeycomb lattice. Our study reveals a striking phase transition between two nontrivial topological phases characterized by gapless flat band with extensive degeneracy. Furthermore, we develop a gauge-invariant mean-field theory for interacting Majorana orbitals, leading to a fractional Chern state. Our work establishes a general framework for gauge-mediated tight-binding models and a gauge-invariant mean-field theory for interacting fractional orbitals that can be readily extended to U(1), SU(N) lattice gauge theories.http://doi.org/10.1103/37kh-kc81 |
| spellingShingle | K. B. Yogendra G. Baskaran Tanmoy Das Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands Physical Review X |
| title | Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands |
| title_full | Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands |
| title_fullStr | Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands |
| title_full_unstemmed | Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands |
| title_short | Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands |
| title_sort | fractional wannier orbitals and tight binding gauge fields in kitaev honeycomb superlattices with flat majorana bands |
| url | http://doi.org/10.1103/37kh-kc81 |
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