Fermionization and Hubbard Models

Abstract

We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this method on various integrable and non-integrable chains, and deduce some general results. In particular, we fermionize XXC spin-chains and study their symmetries. Fermionic realizations of certain Lie algebras and superalgebras appear naturally as symmetries of some models. We also fermionize recently obtained Hubbard models, and obtain for the first time multispecies analogues of the Hubbard model, in their fermionic form. We comment on the conflict between symmetry enhancement and integrability of these models. Finally, the fermionic versions of the non integrable spin-1 and spin-3/2 Heisenberg chains are obtained.

24 pages, Latex. Minor typos corrected, one equation added

References in corpus (8)

• The su(N) XX model
• Fermionic representations of integrable lattice systems
• The su(N) Hubbard model
• Exact integrability of the su(n) Hubbard model
• The XXC Models
• SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model
• Hubbard Models as Fusion Products of Free Fermions
• Lax pair for SU(n) Hubbard model

Cited by in corpus (9)

• Solution of the quantum inverse problem
• Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-S
• Quantum Simulation of the N flavor Gross-Neveu Model
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• New integrable model of correlated electrons with off-diagonal long-range order from $so(5)$ symmetry
• Bethe ansatz for the SU(4) extension of the Hubbard Model
• Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains
• New Integrable Models from Fusion
• Non-additive fusion, Hubbard models and non-locality