2024/07/17 by Yogendra, K. B., Baskaran, G., Das, Tanmoy · 1 citation
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el) #Superconductivity (cond-mat.supr-con)
paper · doi:10.48550/arxiv.2407.12559
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-like 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 non-trivial 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 correlation-induced 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.