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Solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-12 magnets

Sumiran Pujari*

  • *Contact author: sumiran.pujari@iitb.ac.in (on sabbatical leave)
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Phys. Rev. B 111, 214421 – Published 12 June, 2025

DOI: https://doi.org/10.1103/ms6z-729g

Abstract

We write down a class of two-dimensional quantum spin-12 Hamiltonians whose eigenspectra are exactly solvable via the Jordan-Wigner transformation. The general structure corresponds to a suitable grid composed of XY or X-Ising spin chains and Z-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.

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Phys. Rev. B 111, 214421– Published 12 June, 2025
  • Received 24 June 2024
  • Revised 5 February 2025
  • Accepted 15 May 2025
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