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Journal of Physics Condensed Matter

High-spin magnetic states in the two-orbital Hubbard model on a tetrahedron

Alfonso Romano, Canio Noce, Maria Emilia Amendola

Published Oct 21, 2008• 2 citations
Publisher

Abstract

We present a study of the two-orbital degenerate Hubbard model in which the exact numerical solution on a regular tetrahedron is obtained via suitable implementation of the symmetries generated by the spin, the pairing and the orbital pseudospin operators. In particular, we show that a large variety of high-spin magnetic ground states can develop away from half filling, depending on the values of the electron density and the parameters of the model. As the tetrahedron is the simplest finite-size cluster where hopping processes connect all pairs of sites with constant probability, the study is extended by providing the exact analytical solution of the model on an infinite lattice in the unconstrained hopping limit.

DOI
10.1088/0953-8984/20/46/465216

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We present a study of the two-orbital degenerate Hubbard model in which the exact numerical solution on a regular tetrahedron is obtained via suitable implementation of the symmetries generated by the spin, the pairing and the orbital pseudospin operators. In particular, we show that a large variety of high-spin magnetic ground states can develop away from half filling, depending on the values of the electron density and the parameters of the model. As the tetrahedron is the simplest finite-size cluster where hopping processes connect all pairs of sites with constant probability, the study is extended by providing the exact analytical solution of the model on an infinite lattice in the unconstrained hopping limit.
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We present the exact solution of the simplified Hubbard model in which only one kind of electrons can hop and this quantum mechanical hopping of electrons is assumed to be unconstrained. It is shown that the model still behaves non-trivially, although it no longer depends on the lattice structure and the dimensionality of the system. For this case we find: (i) a gap in the ground state energy always exists at the half-filled band point (n = 1), (ii) a preferred magnetic state at n = 1 and large U is a total spin singlet, (iii) U-dependence of the ground state energy has qualitatively the same form as one of the conventional Hubbard model with the (t2/U)-behavior at large U. A phase diagram of the model is discussed.
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The Hubbard model for electrons with orbital degeneracy is shown to have an underlying SUd(4){\mathrm{SU}}_{d}(4)SUd​(4) symmetry of spin-orbital double. A hidden charge SUc(4){\mathrm{SU}}_{c}(4)SUc​(4) symmetry is exposed and an extended Lieb-Mattis transformation, which maps these two symmetries into each other, is given. On the basis of elementary degenerate perturbative theory, it is shown that the system with strong repulsive coupling is equivalent to a SO(6)\mathrm{SO}(6)SO(6) Heisenberg magnet at half-filling and a SU(4)\mathrm{SU}(4)SU(4) one at quarter-filling. The band is half-filled at all temperature for $\ensuremath{\mu}=3U/2.$ The features of ground-state and low-lying excitations in one dimension are indicated according to exact solutions.
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron-hopping terms, the ground state has Ising-type N\'eel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.
The ground-state properties of a simple model for transition metal oxide compounds in ferromagnetic phase have been studied. This model only contains the orbital degree of freedom. The two-orbital spinless Hubbard model in the limit of strong on-site coulomb interaction (U) has been used to describe the motion of election in e[subscript g] orbital. In the large-U and half-filling limits, the effective Hamilto-nian has been derived from the Hubbard model by the canonical transformation. After the transformation, the doubly occupied states have been projected out and the size of the Hillbert space has been reduced. For this effective Hamiltonian, the hopping amplitudes have been defined according to the managanite system which consists of three axes: x-, y- and z-axis. Since the ground-state properties of the effective Hamiltonian have been calculated only in one-dimension, then the results of this work have been separated in three cases; the electrons hopping in x, y, and z axes respectively. The ground-state wavefunction of this effective Hamiltionian has been calculated by infinite density matrix renormalization group algorithm. This algorithm leads to the ground state at the thermodynamic limit when the number of sties is large. It has been found that the ground-state energies are equivalent in all hopping axes. Furthermore, the nearest neighbor orbital correlations at the ground state for all axes are antiferro-orbital.