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International Journal of Modern Physics B

The Behavior of the Critical Magnetic Field and Correlation Functions in Finite-Size Hubbard-Like Models

ARMEN N. KOCHARIAN

Published Jan 20, 1997• 0 citations
Publisher

Abstract

We present exact analytical results for a critical field and correlations functions for N site ring and arbitrary size two dimensional coupled chains in a two component Hubbard model with a strong magnetic field and exactly at half-filling. The critical field near the Nagaoka instability with one spin and two spin flips is driven by Coulomb interaction, lattice geometry, dimensionality and crucially depends on the number of atomic sites N. Unsaturated ferromagnetism, reminiscent of Nagaoka-like behavior, and spin liquid state are examined in the structure of off-diagonal spin correlation at large U.

DOI
10.1142/s0217979297000198

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We present exact analytical results for a critical field and correlations functions for N site ring and arbitrary size two dimensional coupled chains in a two component Hubbard model with a strong magnetic field and exactly at half-filling. The critical field near the Nagaoka instability with one spin and two spin flips is driven by Coulomb interaction, lattice geometry, dimensionality and crucially depends on the number of atomic sites N. Unsaturated ferromagnetism, reminiscent of Nagaoka-like behavior, and spin liquid state are examined in the structure of off-diagonal spin correlation at large U.
We consider two-component Hubbard models in a strong magnetic field to reveal finite-size effects in the stability of the fully polarized state against one- and two-spin flips. Also established are the criteria for unsaturated ferromagnetism, with Smax{\mathit{S}}_{\mathrm{max}}Smax​ and Sz{\mathit{S}}^{\mathit{z}}Sz reduced, depending on the relative signs of hopping parameters. The behavior of the critical field for periodic chains with arbitrary length at half filling is driven by Coulomb interaction, lattice frustration, and crucially band curvature. Unsaturated ferromagnetism, reminiscent of Nagaoka-like behavior, and the influence of spin liquid states are examined in the structure of off-diagonal spin correlations at large U. \textcopyright{} 1996 The American Physical Society.
Ferromagnetic domains in the large-UUU Hubbard model with a few holes: an FCIQMC study
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
Two-dimensional Hubbard lattices with two or three holes are investigated as a function of UUU in the large-UUU limit. In the so-called Nagaoka limit (one-hole system at infinite UUU), it is known that the Hubbard model exhibits a ferromagnetic ground state. Here, by means of exact full configuration interaction quantum Monte Carlo simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing UUU. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centered on individual holes. The overall total spin of the wave functions remains the lowest possible (0 or 12\frac{1}{2}21​, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than 1) number of holes.
With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.
We investigate the magnetization of the ground state of the one-dimensional flat-band Hubbard model as a function of the electron filling, using exact diagonalization techniques. Our calculation shows that the systems with odd n holes added to half-filling bands for a sufficiently large U (the on-site Coulomb repulsion energy) have a saturated ferromagnetic ground state, which is nondegenerate except for the trivial spin degeneracy. Dependences of the critical value of U on the size and on λ (a parameter of the system) are also investigated. For all values of λ, it is found that the ground state is a saturated ferromagnetic state if U is sufficiently large. Moreover, we find that the critical U for the saturated ferromagnetic ground state is almost independent on the system size, at least, for the system near quarter-filling. These facts indicate that even if the system size go to infinity, the ferromagnetic ground state can be exist for a finite U .