Majorana Spin Liquids on a two-leg ladder

TL;DR

This paper constructs and analyzes exactly solvable models of gapless Majorana liquids on a two-leg ladder, revealing stable spin and orbital liquid states with multiple gapless modes and power-law correlations.

Contribution

It introduces new Kitaev-type models realizing Majorana orbital and spin liquids with multiple gapless modes and studies their stability against perturbations.

Findings

MOL has one gapless mode with power-law correlations

SU(2) MSL has three gapless modes with diverse correlations

Both states remain stable under certain perturbations and gauge fluctuations

Abstract

We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power law correlations in energy at incommensuare wavevectors, while the SU(2) MSL has three gapless modes and power law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist upon allowing $Z_2$ gauge field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.