Majorana Spin Liquids on a two-leg ladder

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.

15 pages, 6 figures. Revised version

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• Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Gauging the Kitaev chain
• Majorana states in inhomogeneous spin ladders
• Majorana spin liquids and projective realization of SU(2) spin symmetry
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Vortex Loops and Majoranas
• Engineering Quantum Spin Liquids and Many-Body Majorana States with a Driven Superconducting Box Circuit
• Ground state of a spin-1/2 Heisenberg-Ising two-leg ladder with XYZ intra-rung coupling
• Fractionalized holes in one-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to fermion matter -- deconfined dynamics and emergent integrability
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Topological phases of the compass ladder model