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Phase Transitions

η-pairing superconductivity in generalized Hubbard models

Andreas Schadschneider

Published Jun 1, 1996• 0 citations
Publisher

Abstract

We consider generalized Hubbard models in arbitrary dimensions which have additional nearest-neighbour interactions. It is shown that in a large region of the parameter space these models have ground states of the η-pairing type. These ground states exhibit off-diagonal long-range order and are thus superconducting. In special cases the complete (T=0) phase diagram can be obtained.

DOI
10.1080/01411599608214642

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We consider generalized Hubbard models in arbitrary dimensions which have additional nearest-neighbour interactions. It is shown that in a large region of the parameter space these models have ground states of the η-pairing type. These ground states exhibit off-diagonal long-range order and are thus superconducting. In special cases the complete (T=0) phase diagram can be obtained.
We consider extended versions of the Hubbard model which contain additional interactions between nearest neighbors. In this Letter we show that a large class of these models has a superconducting ground state in arbitrary dimensions. In some special cases we are able to find the complete phase diagram. The superconducting phase exists even for moderate repulsive values of the Hubbard interaction UUU.
We present a new model describing strongly correlated electrons on a general d-dimensional lattice. It is an extended Hubbard model and it contains the t-J model as a special case. The model naturally describes local electron pairs, which can move coherently at arbitrary momentum. By using an \ensuremath{\eta}-pairing mechanism we can construct eigenstates of the Hamiltonian with off-diagonal long-range order. In the attractive case the exact ground state is superconducting in any number of dimensions. On a one-dimensional lattice, the model is exactly solvable by Bethe ansatz.
We consider NNN-particle generalizations of $\ensuremath{\eta}$-pairing states in a chain of NNN-component fermions and show that these states are exact (high-energy) eigenstates of an extended SU(N)\mathrm{SU}(N)SU(N) Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd NNN. When NNN is even, these states exhibit off-diagonal long-range order in NNN-particle reduced density matrix. On the other hand, when NNN is odd, the correlations decay exponentially with distance in the bulk, but end-to-end correlations do not vanish in the thermodynamic limit. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.