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De Gruyter eBooks

On the Definition of the Current Operator Application to the Hubbard Model

J. Monecke

Published Dec 31, 1974• 0 citations
Publisher
DOI
10.1515/9783112501986-010

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Abstract A disagreement existing in the literature between various calculations of the electrical conductivity in the single‐band Hubbard model is resolved. The error, which occurs in a paper by Monecke, is pointed out and explained to be due to the assumption that the current operator, defined as the commutator of the Hubbard Hamiltonian with the polarization operator, is invariant under the lattice translations. The existence of ambiguity in the definition of a “good” current operator (which is translationally invariant) is pointed out and resolved in a large class of situations.
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.