Free fermions beyond Jordan and Wigner
arXiv:2310.19897 · doi:10.21468/SciPostPhys.16.4.102
Abstract
The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows from the eigenvalues of a matrix whose size grows only linearly with the volume of the system. However, several Hamiltonians that do not admit a Jordan-Wigner transformation to fermion bilinears still have the same type of free-fermion spectra. The spectra of such ``free fermions in disguise" models can be found exactly by an intricate but explicit construction of the raising and lowering operators. We generalise the methods further to find a family of such spin chains. We compute the exact spectrum, and generalise an elegant graph-theory construction. We also explain how this family admits an N=2 lattice supersymmetry.
arXiv comment24 pages. v3: title changed
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- A Graph-Theoretic Framework for Free-Parafermion Solvability
- A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets
- The Hilbert-space structure of free fermions in disguise
- Expanding the Class of Free Fermions via Twin-Collapse Methods
- Noninteracting tight-binding models for Fock parafermions
- Periodic revivals from supersymmetry in a fermionic kinetically constrained model