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Physical review. B, Condensed matter

Magnetic properties of multiband U=∞ Hubbard model on anisotropic triangular and rectangular lattice strips

Vladyslav O. Cheranovskii, Okan Esentürk, H. Önder Pamuk

Published Nov 1, 1998• 11 citations
Publisher

Abstract

We study the dependence of the ground state spin of a multiband Hubbard model with infinite electron repulsion on anisotropic triangular and rectangular lattice strips on the model parameters. Considering the results of numerical calculations for the exact spectra of finite triangular lattice strips at different values of hopping integrals, we show the existence of a type of magnetic transitions with the jump of the ground state spin between minimal and maximal values. This transition is found only for special filling factors and when the lattice anisotropy parameter takes some critical value, which depends on the size of the lattice strip. Near this critical point two states with marginal values of the total spin, both of which can be a ground state before or after the transition, are locally stable against a few flips of spins.

DOI
10.1103/physrevb.58.12260

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We study the dependence of the ground state spin of a multiband Hubbard model with infinite electron repulsion on anisotropic triangular and rectangular lattice strips on the model parameters. Considering the results of numerical calculations for the exact spectra of finite triangular lattice strips at different values of hopping integrals, we show the existence of a type of magnetic transitions with the jump of the ground state spin between minimal and maximal values. This transition is found only for special filling factors and when the lattice anisotropy parameter takes some critical value, which depends on the size of the lattice strip. Near this critical point two states with marginal values of the total spin, both of which can be a ground state before or after the transition, are locally stable against a few flips of spins.
The estimations of the stability region of the lattice ferromagnetic ground state in the space of model parameters are found. For the triangular lattice strip formed by L segments with the total number of electrons N=L+1 we derived the effective Hamiltonians describing the low-energy states of the strips and obtained the analytical estimations for above stability region. The possibility of the magnetic transition with the jump of the ground-state spin between minimal and maximal values has also been shown. For the strip with N=L and an alternating value of the one-site potential energy, we have obtained the exact relation between electron parameters, which provides the ferromagnetic character of the lattice ground state. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 253–259, 2001
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We study the ground state in a quasi-one-dimensional triangular Hubbard model using the exact numerical diagonalization, the constrained-path Monte Carlo, and the cluster perturbation theory. As the frustration hopping ttt is small the system exhibits short-range antiferromagnetic correlation. As ttt is greater than a critical point tc{t}_{c}tc​, there is a transition from an antiferromagnetic state to a frustrated state, which is accompanied by a jump of local entanglement and an abrupt change of spin correlation. As ttt is greater than another critical point ${t}_{{c}^{\ensuremath{'}}}$, the insulator-metal transition takes place. The successive order of two transitions depends on the on-site Coulomb interaction. The calculated spectra indicates that the spin-charge separation is destroyed by the frustration hopping. The frustrated state corresponds to the appearance of an additional dispersion band near the Fermi surface.
One-band Hubbard model with transverse anisotropy is considered at density of electrons n=0.4n=0.4n=0.4. It is shown that when the anisotropy is appropriately chosen, the ground state is ferromagnetic with magnetic order perpendicular to the anisotropy. The increasing of the ratio tU\frac tUUt​, where ttt is the hopping parameter and UUU is the Coulomb repulsion, decreases the Curie temperature, and the system arrives at the quantum critical point (TC=0)(T_C=0)(TC​=0). The result is obtained introducing Schwinger bosons and slave Fermions representation of the electron operators. Integrating out the spin-singlet Fermi fields an effective Heisenberg model with ferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Owing to the anisotropy, the magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order.
We investigate the ground-state magnetic properties of the Hubbard model on a two-leg ladder with interchain Coulomb repulsion. When both the on-site and the interchain Coulomb repulsions are infinitely large, we show exactly that the model exhibits saturated ferromagnetism in the ground states for the electron filling factor 1/4<n<1/2.1/4<n<1/2.1/4<n<1/2. The explicit expression of the saturated ferromagnetic ground state is also obtained. By using numerical calculations, we find that ferromagnetism remains stable for sufficiently large values of these interactions, and that the interchain Coulomb repulsion induces tendencies to ferromagnetism, especially on the 1/4-filling side for small values of the interchain hopping parameter.