Canonical representation for electrons and its application to the Hubbard model

Abstract

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 emerges simply by decoupling the Pauli subsystem from the spinless fermion bath. This exchange correctly reproduces the large $U$ superexchange. Also derived, for $U=\pm \infty$, is the Hamiltonian to study Nagaoka ferromagnetism. In this representation, the infinite-$U$ Hubbard problem becomes elegant and easier to handle. Interestingly, the ferromagnetism in Hubbard model is found to be related to the gauge invariance of the spinless fermions. 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 appendices.

10+ pages, 3 Figures

References in corpus (6)

• Correlated Electrons in High Temperature Superconductors
• Quantum Cluster Theories
• Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model
• Fermion-Spin Transformation to Implement the Charge-Spin Separation
• Majorana Fermion Representation For An Antiferromagnetic Spin-1/2 Chain
• Uncertainty Principle Enhanced Pairing Correlations in Projected Fermi Systems Near Half Filling

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