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Physical review. B./Physical review. B

Bond formation effects on the metal-insulator transition in the half-filled kagome Hubbard model

亮太 比嘉, Kenichi Asano

Published Jun 9, 2016• 12 citations
Publisher

Abstract

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 $S=1/2$ 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 $S=1/2$ spins, which are consistent with the ground states of the Kagome antiferromagnet.

DOI
10.1103/physrevb.93.245123

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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.
We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the noninteracting theory at half filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states---a dimer valence bond solid Mott insulator when intertriangle correlations dominate, and a broken C3{C}_{3}C3​-symmetry antiferromagnet that arises from frustration when intratriangle correlations dominate. The metal-insulator transitions into these two phases have very different characters. The metal-broken C3{C}_{3}C3​ antiferromagnetic transition is driven by spontaneous C3{C}_{3}C3​ symmetry breaking that lifts the topologically required degeneracy at the Fermi energy and opens an energy gap in the quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no symmetries of the Hamiltonian. It is caused by strong correlations renormalizing the electronic structure into a phase that is adiabatically connected to both the trivial band insulator and the ground state of the spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither of these metal-insulator transitions can be understood in either the Brinkmann-Rice or Slater paradigms.
We investigate the kagome lattice Hubbard model at half filling using the variational Monte Carlo method by testing the U(1)U(1)U(1)-Dirac spin-liquid, uniform, and valence bond crystal states. Even for the large-UUU case, the U(1)U(1)U(1) Dirac state, which is the optimal state in the Heisenberg model, cannot be recovered. While the finite-UUU Hubbard model allows for the introduction of vacancies in a different manner compared to the $t\text{\ensuremath{-}}J$ model, the physics appears to have many similarities. In particular, a valence bond crystal is formed in the intermediate-UUU regime. We observe an impact of the formation of this valence bond crystal on a possible Mott transition in this model and discuss the properties of the wave function.
The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-cluster expansion and the determinant quantum Monte Carlo, to study the extent as well as doping and interaction dependence of ferromagnetic correlations and other thermodynamic properties of the model. We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength, extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling. These results improve our understanding of the magnetic tendencies of the model away from half filling and pave the way for further studies, including with ultracold atoms in optical lattices.
Motivated by the recent discovery of metallic kagome lattice materials, AV3Sb5{\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}AV3​Sb5​ (A = K, Rb, Cs), we investigate the ground state of the half-filled kagome lattice Hubbard model by employing the density-matrix renormalization group method. We identify a metal-insulator transition around $U\ensuremath{\sim}{U}_{c1}$ and four distinct phases as a function of U/tU/tU/t on narrower cylinders, including a metallic phase at U<Uc1U<{U}_{c1}U<Uc1​, two insulating intermediate phases (a translational symmetry breaking phase at Uc1<U<Uc2{U}_{c1}<U<{U}_{c2}Uc1​<U<Uc2​ and a quantum spin liquid phase at Uc2<U<Uc3{U}_{c2}<U<{U}_{c3}Uc2​<U<Uc3​), and the kagome antiferromagnetic phase at U>Uc3U>{U}_{c3}U>Uc3​. We confirm that the translational symmetry breaking phase is robust for wider cylinders, while the quantum spin liquid phase is smoothly connected to the kagome antiferromagnetic phase with increasing the system width. Moreover, our numerical observations indicate a continuous metal-insulator transition at Uc1{U}_{c1}Uc1​ whose nature is consistent with Slater's transition scenario. The magnetic phase transition between two insulating intermediate phases at Uc2{U}_{c2}Uc2​ is first order. Our findings may provide insights into exotic kagome lattice materials.
Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8, we study a single-band extended Hubbard model on an anisotropic Kagome lattice with the 1/6 electron filling. Due to the partial filling of the lattice, the inter-site repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters, rather than at lattice sites. We provide examples of such cluster Mott insulators and study the phase transitions between metallic states and cluster Mott insulators on an anisotropic Kagome lattice. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. However, the nature of charge excitations in different cluster Mott insulators could be quite different and we show that there exists a novel cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 1/3 of the total spinon excitations are magnetically active. The strong coupling limit of the same model is also analyzed via a Kugel-Khomskii-like model. Based on these results, we propose that the anomalous behavior of the finite-temperature spin-susceptibility in LiZn2Mo3O8 may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.