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Journal of Physics Condensed Matter

Mott transition of correlated electrons on the Kagomé lattice

Syunsuke Kuratani, Akihisa Koga, Norio Kawakami

Published Mar 23, 2007• 9 citations
Publisher

Abstract

We investigate the stability of the metallic state in the Hubbard model on the Kagom? lattice at half filling. By means of the variational Monte?Carlo simulations including onsite and nearest neighbour doublon?holon correlations, we clarify that the Mott transition occurs at Uc~11.5t in the system at zero temperature, which is consistent with the recent results obtained by the dynamical cluster approximation. The stability of the Mott insulating state is also addressed.

DOI
10.1088/0953-8984/19/14/145252

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We investigate the stability of the metallic state in the Hubbard model on the Kagom? lattice at half filling. By means of the variational Monte?Carlo simulations including onsite and nearest neighbour doublon?holon correlations, we clarify that the Mott transition occurs at Uc~11.5t in the system at zero temperature, which is consistent with the recent results obtained by the dynamical cluster approximation. The stability of the Mott insulating state is also addressed.
We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc ≈ 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.
The aim of this thesis is the investigation of electronic correlations in the intermediate region between the metallic and insulating phase of the frustrated Kagome lattice. Most previous studies address the ground state of the Heisenberg model on the Kagome lattice, and therefore only the purely insulating phase. However, we go a step further by studying the Hubbard model on the Kagome lattice and thus including metallic contributions. We solve the Hubbard model with the determinant quantum Monte Carlo (DQMC) method and compare to results of the dynamical mean field theory (DMFT). First we study the half-filled system across the range of the Mott-Hubbard metal-insulator transition, and then the electron doped system, where the chemical potential is in the center of the flat band. In various post-processing steps we calculate the k-integrated spectral functions, the k-resolved spectral functions, the equal-time magnetic structure factors and the dynamic magnetic structure factors.
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.
Dynamics in a triangular-lattice Hubbard model is studied at half filling on the basis of the cluster dynamical mean field theory. Numerical calculations use a solver of the continuous-time quantum Monte Carlo method based on the strong-coupling expansion. We examine the change in the nearest-neighbor dynamical correlations of doublon and holon in the time domain with varying the Coulomb repulsion near the Mott transition. We demonstrate that the nearest-neighbor doublon-holon pair shows a strong attractive correlation, particularly in the insulating phase, while the nearest-neighbor doublon-doublon pair shows a repulsive correlation. Useful information is provided by the trajectories in the complex plane of the dynamical correlation functions. The short-time dynamics of the nearest-neighbor doublon and holon in the metallic phase indicates larger fluctuations than in the insulating phase. Their trajectories in the complex plane show that the short-time dynamics of the doublon-holon pair has an opposite behavior to that of the doublon-doublon pair. We find that their time scale of dynamics can be characterized by the period in which the phase rotates π around the long-time limit in both phases. In the long-time region, fluctuations persist up to a very long time in the metallic phase, while they quickly vanish in the insulating phase.
We study the metal-insulator transition in the half-filled Hubbard model on a Kagome lattice using the variational cluster approximation. The strong coupling limit of the model corresponds to the S=1/2S=1/2S=1/2 Kagome Heisenberg antiferromagnet, which is known to have a singlet ground state, although its detail is still debated. As the results of the cluster methods generally depend much on the choice of the unit cluster, we have chosen the clusters that are compatible with these singlet ground states in the strong coupling case found so far, which basically consist of even number of sites. It is found that the correlated electrons on the Kagome lattice have a strong tendency to form valence-bond structures, which are the resonation of electrons on a single bond or several bonds forming loops. The zero-temperature metal-insulator transition at some interaction strength is possibly driven by the formation of such short range valence bonds and shows a second order character, which is distinctive from the Brinkman-Rice scenario. The electrons on these valence bonds further localizes onto each site as the interaction increases, and the valence bonds of electrons finally turn into magnetic singlet bonds between localized S=1/2S=1/2S=1/2 spins, which are consistent with the ground states of the Kagome antiferromagnet.