arXiv:cond-mat/0306495

Something about spin-fermion connection

Stanislav V. Dobrov

Published Jun 19, 2003• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.cond-mat/0306495

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arXiv:cond-mat/0306495

Something about spin-fermion connection

Stanislav V. Dobrov

Published Jun 19, 2003• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/0306495

Related papers

On the spin–fermion connection

Stanislav V. Dobrov

Journal of Physics A Mathematical and GeneralSep 15, 200310 citations

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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

Jordan-Wigner transformation in a higher-dimensional lattice

Wang Shaofeng

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsFeb 1, 199511 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.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

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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.

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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.