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Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior [1]. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density. By the same technique exact ground states are constructed for triangle and pentagon Hubbard chains. The results for the triangle chain permit direct comparison with results obtained by variational techniques for the one-dimensional periodic Anderson model with next-nearest neighbor hybridization [2] and provide a mechanism for ferromagnetism in CeRh3B2. The technique for the construction of exact ground states requires (i) a re-writing of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension and requires no integrability but only sufficiently many microscopic parameters in the Hamiltonian so that an exact solution can be found on a hypersurface in parameter space. It was previously used [3] to construct a class of exact metallic and insulating ground states of the three-dimensional periodic Anderson model on regular Bravais lattices at and above 3/4. The metallic phase is a non-Fermi liquid with one dispersing and one flat band.
[1] Z. Gulacsi, A. Kampf, and D. Vollhardt, Phys. Rev. Lett. 99, 026404 (2007). [2] H. N. Kono and Y. Kuramoto, J. Phys. Soc. Jpn. 75, 084706 (2006). [3] Z. Gulacsi and D. Vollhardt, Phys. Rev. Lett. 91, 186401 (2003); Phys. Rev. B 72, 075130 (2005). |
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