Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids

TL;DR

This paper introduces exactly solvable 2D spin-orbital models that exhibit diverse quantum disordered phases with Majorana fermions, flat bands, and topological transitions, providing new insights into exotic spin-orbital-liquid states.

Contribution

It presents a class of exactly solvable spin-orbital models with tunable topological and flat band features, extending the understanding of quantum disordered phases in spin-orbital systems.

Findings

Majorana fermions with Fermi surfaces and Dirac points identified

Magnetic fields induce flux pattern stabilization and topological transitions

Biquadratic perturbations stabilize zero-energy flat bands

Abstract

Spin-orbital liquids are quantum disordered states in systems with entangled spin and orbital degrees of freedom. We study exactly solvable spin-orbital models in two dimensions with selected Heisenberg-, Kitaev-, and $\Gamma$-type interactions, as well as external magnetic fields. These models realize a variety of spin-orbital-liquid phases featuring dispersing Majorana fermions with Fermi surfaces, nodal Dirac or quadratic band touching points, or full gaps. In particular, we show that Zeeman magnetic fields can stabilize nontrivial flux patterns and induce metamagnetic transitions between states with different topological character. Solvable nearest-neighbor biquadratic spin-orbital perturbations can be tuned to stabilize zero-energy flat bands. We discuss in detail the examples of $\mathrm{SO}(2)$- and $\mathrm{SO}(3)$-symmetric spin-orbital models on the square and honeycomb lattices, and use group-theoretical arguments to generalize to $\mathrm{SO}(\nu)$-symmetric models with arbitrary integer $\nu > 1$. These results extend the list of exactly solvable models with spin-orbital-liquid ground states and highlight the intriguing general features of such exotic phases. Our models are thus excellent starting points for more realistic modellings of candidate materials.