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Journal of Physics Conference Series

Effect of the repulsion interaction on the ground-state of the Kondo lattice model with a superlattice potential

Jereson Silva-Valencia, R Franco, Marcos Sergio Figueira

Published Apr 1, 2014• 0 citations
Publisher

Abstract

We investigate the ground-state of a new Kondo lattice model, where the free carriers interact repulsively between them and undergo an external superlattice potential. This model can be simulated with 171 Yb atoms confined in optical lattices. We use the density matrix renormalization group method to evaluate the charge and spin gaps, and the structure factors. We found that the ground-state evolves from a Kondo spin liquid state to a charge-gapped antiferromagnetic state with zero spin gap, when the antiferromagnetic exchange increases. Also, we verify that the quantum critical point varies linearly with the repulsion and the exchange.

DOI
10.1088/1742-6596/480/1/012015

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We investigate the ground-state of a new Kondo lattice model, where the free carriers interact repulsively between them and undergo an external superlattice potential. This model can be simulated with 171 Yb atoms confined in optical lattices. We use the density matrix renormalization group method to evaluate the charge and spin gaps, and the structure factors. We found that the ground-state evolves from a Kondo spin liquid state to a charge-gapped antiferromagnetic state with zero spin gap, when the antiferromagnetic exchange increases. Also, we verify that the quantum critical point varies linearly with the repulsion and the exchange.
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We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange JJJ. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as JJJ increases, the spin-charge couplings become important and the critical point Uc{U}_{c}Uc​ is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.
The density-matrix renormalization-group method is applied to the one-dimensional Kondo-lattice model with the Coulomb interaction between the conduction electrons. The spin and charge gaps are calculated as a function of the exchange constant JJJ and the Coulomb interaction Uc{U}_{c}Uc​. It is shown that both the spin and charge gaps increase with increasing JJJ and Uc{U}_{c}Uc​. The spin gap vanishes in the limit of $J\ensuremath{\rightarrow}0$ for any Uc{U}_{c}Uc​ with an exponential form, ${\ensuremath{\Delta}}_{s}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\frac{1}{\ensuremath{\alpha}({U}_{c})J\ensuremath{\rho}}]$. The exponent, $\ensuremath{\alpha}({U}_{c})$, is determined as a function of Uc{U}_{c}Uc​. The charge gap is generally much larger than the spin gap. In the limit of $J\ensuremath{\rightarrow}0$, the charge gap vanishes as ${\ensuremath{\Delta}}_{c}=\frac{1}{2}J$ for Uc=0{U}_{c}=0Uc​=0 but for a finite Uc{U}_{c}Uc​ it tends to a finite value, which is the charge gap of the Hubbard model.
We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter $\ensuremath{\eta}$ in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with $\ensuremath{\eta}$, but when $\ensuremath{\eta}$ approaches zero, they drop abruptly.