arXiv subjects

K. B. Yogendra

Publications and source records attributed to K. B. Yogendra.

3 recordsLinked to original sources

arXiv2025

Fractional Wannier Orbitals and Tight-Binding Gauge Fields for 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 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 $Z_2$ 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 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.

cond-mat.str-el↗

arXiv2024

Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets

Classical magnets exhibit exotic ground state properties such as spin liquids and fractionalization, promising a manifestation of superposition and projective symmetry construction in classical theory. While system-specific spin-ice or soft-spin models exist, a formal theory for general classical magnets remains elusive. Here, we introduce a generic symmetry group construction built from a vector field in a plaquette of classical spins, demonstrating how classical spins superpose in irreducible representations (irreps) of the symmetry group. The corresponding probability amplitudes serve as order parameters and local spins as fragmented excitations. The formalism offers a many-body vector field representation of diverse ground states, including spin liquids and fragmented phases described as degenerate ensembles of irreps. We apply the theory to a frustrated square Kagome lattice, where spin-ice or soft spin rules are inapt, to describe spin liquids and fragmented phases, all validated through irreps ensembles and unbiased Monte Carlo simulation. Our generic theory sheds light on previously unknown aspects of spin-liquid phases and fragmentation and broadens their applications to other branches of field theory.

cond-mat.str-el↗

arXiv2023

Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting

The complete phase diagram of the Kitaev model with a magnetic field remains elusive, as do the experimental results in the candidate material α-RuCl3. Here, we study the Kitaev model on a one-dimensional ladder setting within the density-matrix renormalization group method in the presence of a magnetic field at zero temperature. We find five distinct phases with increasing magnetic field, which are characterized by a homogeneous flux phase, the Z2 vortex gas, solid and emergent glass phase, and finally, a spin-polarized phase. The emergent glassiness is confirmed by calculating correlation functions showing quasi-long-range behavior and ground state fidelity, showing a plethora of energetically accessible orthogonal saddle points corresponding to different flux configurations. This glassy behavior seems to arise from the slow dynamics of the Z2 fluxes, which is a consequence of the local constraints present in the underlying Hilbert space. This phenomenon can also be explored in other spin-liquid systems where the corresponding low-energy excitations are similarly retarded due to constraints.

cond-mat.str-el↗