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Abstract
We focus our quantitative analysis on the stability of insulator state in the Hubbard model at half-filling. Taking into account macroscopic fluctuation of the on-site repulsion, we consider the possibility of realizing a steady state which is characterized by electron pairing. Fluctuation of the on-site repulsion leads to the formation of holes in the form of excited states. The electron liquid has two possibilities of relaxation in the state with bare on-site repulsion U: trivial, to the initial state, and nontrivial to state in which electrons polarize holes forming electron-hole pairs. A steady state is determined by minimum energy for given U and its fluctuation . The values U and , for which the states with electron pairing are stable, are calculated. The proposed pairing mechanism is to some extent similar to the formation of a long-range pairing correlation in an optically induced Hubbard chain [].
Highlights
The Hubbard chain is unstable at half filling occupation, according to the Lieb-Wu solution [2] the fermion spectrum is gapped for arbitrary onsite repulsion [2, 3]
The discovered instability of the Hubbard model at half filling occupation allows us to propose a possible mechanism of electron pairing
To realize such a pairing mechanism, sufficiently large macroscopic fluctuations of the on-site Coulomb repulsion are required, which can occur in low-dimensional systems
Summary
The Hubbard chain is unstable at half filling occupation, according to the Lieb-Wu solution [2] the fermion spectrum is gapped for arbitrary (non equal to zero) onsite repulsion [2, 3]. In 2D and 3D lattices at half filling, the Mott transition in insulator phase is realized at finite value of the on-site Coulomb repulsion [4]. At half filling the low-energy excitations are holes, so the fluctuation of the on-site Coulomb repulsion leads to the formation of holes in the spectrum, which can form pairs with electrons (due to the polarization of holes by electrons). Electron pairing is determined by both values of the bare on-site repulsion and its fluctuation We use this idea to consider the stability of the Hubbard model in the framework of a mean field approach with electron pairing. The phase of the effective field is a new unknown parameter that corresponds to the minimum of action This approach allows one to study the Mott-Hubbard phase transition for an arbitrary dimension of the Hubbard model. It should be noted that the insulator phase disappears in this case since both Hubbard bands are partially filled
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