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arXiv:cond-mat/0008373

Precursory Metal-Insulator transition in a small cluster of the `t-J' model: Exact analytic results

Rogério de Sousa, G. G. Cabrera

Published Aug 24, 2000• 0 citations
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Abstract

We study the effect of hole hopping in a doped antiferromagnet described by the `t-J' model, using exact analytic solutions for small clusters. In spite of the small size, they reveal interesting details about the magnetic order, which are not apparent in Mean Field treatments or in numerical calculations. The 4-site cluster with one hole yields the most interesting physics, displaying different behaviors for the ground state: i) an antiferromagnetic phase for t<>J, we obtain strong ferromagnetic correlations (maximum spin) and no density waves, with quantum fluctuations precluding the saturation of the magnetic moment. This behavior shows traces of a metal-insulator transition as the hole kinetic energy competes with the antiferromagnetic interactions.

DOI
10.48550/arxiv.cond-mat/0008373

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We study the effect of hole hopping in a doped antiferromagnet described by the `t-J' model, using exact analytic solutions for small clusters. In spite of the small size, they reveal interesting details about the magnetic order, which are not apparent in Mean Field treatments or in numerical calculations. The 4-site cluster with one hole yields the most interesting physics, displaying different behaviors for the ground state: i) an antiferromagnetic phase for t<>J, we obtain strong ferromagnetic correlations (maximum spin) and no density waves, with quantum fluctuations precluding the saturation of the magnetic moment. This behavior shows traces of a metal-insulator transition as the hole kinetic energy competes with the antiferromagnetic interactions.
We investigate the metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.
To gain insight into the physics of the metal-insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used 1, 2-, and 4-site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences in spectra (in particular a sharper band edge in the cluster calculation) persist in the strong-coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, as well as for differences in behavior between the single-band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self-energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal-insulator transition. Implications for the theoretical treatment of doped manganites are discussed.
We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest-neighbor hopping t, we also include a next-to-nearest-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small ${\mathit{t}}^{\ensuremath{'}}$/t to a dimerized insulator with a spin gap at larger ${\mathit{t}}^{\ensuremath{'}}$/t. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed. \textcopyright{} 1996 The American Physical Society.
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.
The behavior of the Drude weight is studied in the small-J/t regime of the t-J model by Lanczos diagonalizations of small clusters with arbitrary boundary conditions and a small number of holes. Although the total spin of the ground state in the J/t\ensuremath{\rightarrow}0 limit depends strongly on the boundary conditions, the Drude weight exhibits a rather universal behavior and indicates a sharp transition around J/t\ensuremath{\sim}0.1 for a hole concentration of \ensuremath{\sim}10%. This crossover is interpreted as a paramagnetic-ferromagnetic transition. For J/t larger than the crossover value, the Drude weight is somehow constant (and reduced by a factor \ensuremath{\sim}3 compared to the case of free holes), suggesting that coherent transport is almost insensitive to the variation of the antiferromagnetic correlation length. At small J/t (and finite doping), the exact nature of the ferromagnetic phase is still uncertain, since both fully polarized state or spin-polaron gas are found in small clusters depending on the boundaries.
We report the cluster dynamical mean field theory calculations performed for the ground state of the half filled Hubbard model on a honeycomb lattice with exact diagonalization on the cluster-impurity solver. Through using elaborate numerical analytic continuation, we identify the existence of a ``spin liquid'' from the on-site interaction U=0U=0U=0 to Uc{U}_{c}Uc​ (between 4.6t4.6t4.6t and 4.85t4.85t4.85t) with a smooth crossover correspondingly from the charge fluctuation dominating phase into the charge correlation dominating phase. The semimetallic state exits only at U=0U=0U=0. We further find that the magnetic phase transition at Uc{U}_{c}Uc​ from the spin liquid to the N\'eel antiferromagnetic Mott insulating phase is a first-order quantum phase transition. We also show that the charge fluctuation plays a substantial role on keeping the spin liquid phase against the emergence of a magnetic order.