A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets
arXiv:2406.17034 · doi:10.1103/ms6z-729g
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.
arXiv comment12 pages, 7 figures for journal publication. To appear in Physical Review B
References in corpus (29)
- Anyons in an exactly solved model and beyond
- Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
- Kitaev quantum spin liquid - concept and materialization
- Bose-Einstein Condensation in Magnetic Insulators
- Models and Materials for Generalized Kitaev Magnetism
- Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
- The Flux-Phase of the Half-Filled Band
- Spin Ice, Fractionalization and Topological Order
- Exact solution of the Falicov-Kimball model with dynamical mean-field theory
- Fractional excitations in the square-lattice quantum antiferromagnet
- Thermal fractionalization of quantum spins in a Kitaev model: -linear specific heat and coherent transport of Majorana fermions
- Vaporization of Kitaev spin liquids
- A derivation (and quantification) of the third law of thermodynamics
- 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
- The quantum Ising chain for beginners
- Spatially Anisotropic Heisenberg Kagome Antiferromagnet
- Free fermions behind the disguise
- Characterization of solvable spin models via graph invariants
- Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
- Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
- Orbital order driven quantum criticality
- Geometric Criterion for Solvability of Lattice Spin Systems
- Exact solution of a cluster model with next-nearest-neighbor interaction
- Free fermions beyond Jordan and Wigner
- Generalized Falicov-Kimball Models
- A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
- Magnetization process of a quasi-two-dimensional quantum magnet: Two-step symmetry restoration and dimensional reduction