A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets

Abstract

We write down a class of two-dimensional quantum spin-1/2 Hamiltonians whose eigenspectra are exactly solvable via the Jordan-Wigner transformation. The general structure corresponds to a suitable grid composed of XY or XX-Ising spin chains and ZZ-Ising spin chains and is generalizable to higher dimensions. They can host stacks of one-dimensional spinless fermion liquids with gapless excitations and power-law correlations coexisting with ordered spin moments (localized spinless fermions). Bond-dependent couplings thus can be an alternate mechanism than geometric frustration of SU(2)-symmetric couplings to obtain spinless fermionic excitations. Put in a different way, bond-dependent couplings allow for an embedding of one-dimensional spinless fermion (Tomonoga-Luttinger) liquids and solids and also Majorana excitations in higher dimensions. They can accommodate a simpler set of site-local conserved quantities apart from the more intricate, interlocked set of plaquette-local or bond-local conserved quantities in Kitaev's honeycomb model with Majorana excitations. The proposed grid structure may provide an architecture for quantum engineering with controllable qubits.

12 pages, 7 figures for journal publication. To appear in Physical Review B

References in corpus (11)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Bose-Einstein Condensation in Magnetic Insulators
• Models and Materials for Generalized Kitaev Magnetism
• Fractional excitations in the square-lattice quantum antiferromagnet
• Vaporization of Kitaev spin liquids
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Ordering in spatially anisotropic triangular antiferromagnets
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Spatially Anisotropic Heisenberg Kagome Antiferromagnet
• Orbital order driven quantum criticality
• Magnetization process of a quasi-two-dimensional quantum magnet: Two-step symmetry restoration and dimensional reduction

Cited by in corpus (1)

• «Anticommuting» ${\mathbb{Z}}_2$ quantum spin liquids