Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2407.16403 · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics

Jordan–Wigner transformation constructed for spinful fermions at S=1/2 spins in one dimension

Zsolt Gulácsi

Published Aug 28, 2024• 3 citations
arXivHTMLPDF

Abstract

An exact Jordan–Wigner type of transformation is presented in 1D connecting spin-1/2 operators to spinful canonical Fermi operators. The transformation contains two free parameters allowing a broad interconnection possibility between spin models and fermionic models containing spinful Fermi operators.
DOI
10.1080/14786435.2024.2392703

Related papers

Jordan–Wigner transformation constructed for spinful fermions at spin-1/2 in two dimensions

Zsolt Gulácsi

Recently a Jordan–Wigner transformation was constructed for spinful fermions at S=1/2 spins in one dimension connecting the spin-1/2 operators to genuine spinful canonical Fermi operators. In the presented paper, this exact transformation is generalised to two dimensions.

arXiv:2412.11339•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Feb 21, 2025•1 citation

Spin-1/2 operators exactly mapped to spinful canonical Fermi operators present in two bands

Zsolt Gulácsi

Abstract Recently, it has been shown that the quantum spin–1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [1] and 2D [2] as well. In this paper, using the same technique based on an extended Jordan–Wigner transformation, we show in 1D that the quantum spin-1/2 operators can be exactly transformed also in spinful canonical Fermi operators of spin-1/2 fermions that are belong to two bands.

arXiv:2506.17734•The European Physical Journal B•Jul 1, 2025•0 citations

Fermionization transform for certain higher-dimensional quantum spin models

Victor M. Galitski

Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key steps are to enlarge the Hilbert space of the original model by adding to it a collection of stand-alone free spins and to use a combination of these auxiliary operators and the lattice spins to construct a proper fermion representation of the physical Hamiltonian. The transform is especially useful for lattice spin Hamiltonians, where two-spin interactions of $XY$ type are either absent or exist only within one-dimensional chains and where the chains are coupled via two-spin interactions of Ising type, ring-exchange terms, or more general multispin interactions that involve an even number of spin operators from each chain. Using the proposed fermionization method we provide a simple argument suggesting that a spin Hamiltonian closely related to the ring-exchange model proposed by Paramekanti et al., [Phys. Rev. B 66, 054526 (2002)] indeed realizes a spin-liquid state.

arXiv:1003.3874•Physical Review B•Aug 27, 2010•11 citations

On the spin–fermion connection

Stanislav V. Dobrov

Jordan–Wigner-type transformations connecting the spin-3/2 operators and two types of fermion are derived. The general condition of fermionizability of spins is obtained. Discordances in the results of a previous attempt to generalize the Jordan–Wigner transformation for all spins (Batista and Ortiz 2001 Phys. Rev. Lett. 86 1082) are pointed out. After introducing clarity, a new interpretation is given for these results.

Journal of Physics A Mathematical and General•Sep 15, 2003•10 citations

Something about spin-fermion connection

Stanislav V. Dobrov

Jordan-Wigner-type transformations connecting the spin-3/2 operators and two kinds of fermions are derived. A general condition of fermionizability of spins is obtained and a theorem establishing connection between half integer spins and fermions is proved. The fallibility of a previous attempt to generalize the Jordan-Wigner transformation for all spins (C.D. Batista and G. Ortiz, Phys. Rev. Lett. 86, 1082 (2001)) is pointed out.

arXiv:cond-mat/0306495•Jun 19, 2003•0 citations

Free fermions beyond Jordan and Wigner

Paul Fendley, Balázs Pozsgay

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:2310.19897•SciPost Physics•Apr 10, 2024•11 citations
Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key steps are to enlarge the Hilbert space of the original model by adding to it a collection of stand-alone free spins and to use a combination of these auxiliary operators and the lattice spins to construct a proper fermion representation of the physical Hamiltonian. The transform is especially useful for lattice spin Hamiltonians, where two-spin interactions of XYXYXY type are either absent or exist only within one-dimensional chains and where the chains are coupled via two-spin interactions of Ising type, ring-exchange terms, or more general multispin interactions that involve an even number of spin operators from each chain. Using the proposed fermionization method we provide a simple argument suggesting that a spin Hamiltonian closely related to the ring-exchange model proposed by Paramekanti et al., [Phys. Rev. B 66, 054526 (2002)] indeed realizes a spin-liquid state.
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.