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Journal of Huaibei Industry Teachers College

The Transformation from Pauli Operators into Hubbard Operators

Jun Wu

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We use the unity and orthogonal of Hubbard operators to give the transforming formula of Pauli operators and Hubbard operators,by using these transforming formula we realize the change from Pauli operators to Hubbard operators.We get the Hamiltonian expressed by Hubbard operators of the anisotropic spin-ladder model.

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The Transformation of Hamiltonian of Anisotropic Spin-ladder Model Between Pauli Operators and Hubbard Operators

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This paper used the unity and orthogonal of Hubbard operators to give the transforming formula of Pauli operators and Hubbard operators, by using these transforming formula we realize the change from Pauli operators to Hubbard operators. We get the Hamiltonian of the anisotropic spin-ladder model expressed by Hubbard operators. We use the example to realize the transform between Hubbard operators and Pauli operators.

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A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible, and constraint-free. Importantly, it simplifies the Hubbard interaction. On a bipartite lattice, the Hubbard model is reduced to a form in which the exchange interaction simply emerges by decoupling the Pauli subsystem from the spinless fermion bath. This exchange correctly reproduces the large UUU superexchange. Also derived, for $U=\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, is the Hamiltonian to study Nagaoka ferromagnetism. In this representation, the infinite-UUU Hubbard problem becomes elegant and easier to handle. Interestingly, the ferromagnetism in the Hubbard model is found to be related to the gauge invariance of the spinless fermions. A generalization of this representation for the multicomponent fermions, a new representation for bosons, the notion of a ``soft-core'' fermion, and some interesting unitary transformations are introduced and discussed in the appendixes.
The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.