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Fractional Wannier Orbitals and Tight-Binding Gauge Fields in Kitaev Honeycomb Superlattices with Flat Majorana Bands

K. B. Yogendra1, G. Baskaran2,3,4, and Tanmoy Das1

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Phys. Rev. X 15, 031020 – Published 17 July, 2025

DOI: https://doi.org/10.1103/37kh-kc81

Abstract

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 Z2 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.

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Popular Summary

Fractional quantum excitations, such as Majorana fermions, offer a powerful alternative to conventional spin-based quantum technologies like encryption and teleportation. These exotic particles emerge in quantum spin liquids and are naturally coupled with the underlying gauge fields. However, the lack of workable lattice models has made it difficult to study how Majoranas behave under extreme conditions or to come up with their measurement protocols. In this study, we present a new superexchange method to devise a lattice-gauge model of these particles that captures the essential gauge interactions, quantum geometry, and topology.

We apply this framework to the Kitaev honeycomb model—a well-known, exactly solvable quantum spin model where spin-half particles sit on the vertices of a honeycomb lattice—and uncover new insights into Majorana behavior during topological phase transitions. Unlike conventional transitions that occur at isolated points, the ones we study involve flat bands of Majorana states, meaning an extensive number of states become degenerate. This framework helps in constructing complex, gauge-invariant interactions between Majoranas mediated by a double exchange process. To make sense of these interactions, we develop a new gauge-invariant mean-field theory that predicts fractional Chern insulating states, providing analytical solutions for fractional Chern phases in this exotic system.

This work lays the foundation for studying a broader class of strongly interacting quantum systems governed by gauge theories. It also opens the possibility of exploring more exotic particles like anyons and paraparticles, which are of great interest for advancing next-generation quantum computing and sensing technologies.

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Phys. Rev. X 15, 031020– Published 17 July, 2025
  • Received 6 August 2024
  • Revised 8 February 2025
  • Accepted 12 May 2025
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