Journal of Physics A Mathematical and General

On the spin–fermion connection

Stanislav V. Dobrov

Published Sep 15, 2003• 10 citations

Abstract

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.

DOI: 10.1088/0305-4470/36/39/101

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Journal of Physics A Mathematical and General

On the spin–fermion connection

Stanislav V. Dobrov

Published Sep 15, 2003• 10 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/36/39/101

Related papers

Something about spin-fermion connection

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arXiv:cond-mat/0306495Jun 19, 20030 citations

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

Zsolt Gulácsi

arXiv:2407.16403The Philosophical Magazine A Journal of Theoretical Experimental and Applied PhysicsAug 28, 20243 citations

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

Zsolt Gulácsi

arXiv:2412.11339The Philosophical Magazine A Journal of Theoretical Experimental and Applied PhysicsFeb 21, 20251 citation

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.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.

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A mapping between the spin and fermion algebra

Felix Meier, Daniel Waltner, Petr A. Braun +1 more

Abstract We derive a formalism to express the spin algebra <?CDATA $\mathfrak{s}\mathfrak{u}(2)$ ?> s u ( 2 ) in a spin s representation in terms of the algebra of L fermionic operators that obey the canonical anti-commutation relations. We also give the reverse direction of expressing the fermionic operators as polynomials in the spin operators of a single spin. We extend here to further spin values the previous investigations by Dobrov (2003 J. Phys. A: Math. Gen. 36 L503) who in turn clarified on an inconsistency within a similar formalism in the works of Batista and Ortiz (2001 Phys. Rev. Lett. 86 1082). We then consider a system of L fermion flavors and apply our mapping in order to express it in terms of the spin algebra. Furthermore we investigate a possibility to simplify certain Hamiltonian operators by means of the mapping.Abstract We derive a formalism to express the spin algebra <?CDATA $\mathfrak{s}\mathfrak{u}(2)$?> s u ( 2 ) in a spin s representation in terms of the algebra of L fermionic operators that obey the canonical anti-commutation relations. We also give the reverse direction of expressing the fermionic operators as polynomials in the spin operators of a single spin. We extend here to further spin values the previous investigations by Dobrov (2003 J. Phys. A: Math. Gen. 36 L503) who in turn clarified on an inconsistency within a similar formalism in the works of Batista and Ortiz (2001 Phys. Rev. Lett. 86 1082). We then consider a system of L fermion flavors and apply our mapping in order to express it in terms of the spin algebra. Furthermore we investigate a possibility to simplify certain Hamiltonian operators by means of the mapping.

arXiv:2101.10119Journal of Physics A Mathematical and TheoreticalJul 13, 20210 citations

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.

Abstract We derive a formalism to express the spin algebra <?CDATA

\mathfrak{s}\mathfrak{u}(2)

?> s u ( 2 ) in a spin s representation in terms of the algebra of L fermionic operators that obey the canonical anti-commutation relations. We also give the reverse direction of expressing the fermionic operators as polynomials in the spin operators of a single spin. We extend here to further spin values the previous investigations by Dobrov (2003 J. Phys. A: Math. Gen. 36 L503) who in turn clarified on an inconsistency within a similar formalism in the works of Batista and Ortiz (2001 Phys. Rev. Lett. 86 1082). We then consider a system of L fermion flavors and apply our mapping in order to express it in terms of the spin algebra. Furthermore we investigate a possibility to simplify certain Hamiltonian operators by means of the mapping.