Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

Abstract

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.

7 pages, 6 figures

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Correlated Electrons in High Temperature Superconductors
• Complexity in Strongly Correlated Electronic Systems
• Theory of ultracold Fermi gases
• A Mott insulator of fermionic atoms in an optical lattice
• Discovery of microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x
• Imaging the granular structure of high-Tc superconductivity in underdoped Bi2Sr2CaCu2O8+x
• Entanglement in spatially inhomogeneous many-fermion systems
• Metal-Insulator transition in one-dimensional Hubbard superlattices
• Effects of nanoscale spatial inhomogeneity in strongly correlated systems
• Charge-density waves in one-dimensional Hubbard superlattices
• Competition between local potentials and attractive particle-particle interactions in superlattices

Cited by in corpus (3)

• Ferromagnetism beyond Lieb's theorem
• Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids
• Finite temperatures and flat bands: the Hubbard model on three-dimensional Lieb lattices