In order to study the vortex core electronic structure in high-Tc superconductors, we examine 1-D Hubbard model with trap potential by using the density matrix renormalization group method. Instead of directly treating the vortex, the approach mimics the carrier density depression inside the vortex core via the trap potential and exactly calculate strong correlation effects on the depressed region. Consequently, we find that the Mott state emerges in the central region and the metallic edge surrounds the Mott region. Furthermore, when adding spin imbalance, the calculations reveal that a local antiferromagnetic order covers the Mott state region, and moreover, the antiferromagnetic order modulates with a long periodicity. We expect that these results closely relate to the vortex core electronic structure while their calculation results can be directly compared with atomic Fermi gases loaded on an optical lattice.
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