We discuss the metal-insulator transition of the spinless fermion model on a kagome lattice at 1/3 filling. The system is analyzed by using exact diagonalization, density-matrix renormalization group methods, and random-phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of an effective model, i.e., plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping matrix elements, reflecting the difference in the band structure near the Fermi level.
We discuss the metal-insulator transition of the spinless fermion model on the Kagomé lattice at 1/3-filling. The system is analyzed using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of the effective model with a plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping integrals, reflecting the difference of band structure at the Fermi level.
We study a model of strongly interacting spinless fermions and hard-core bosons on an anisotropic kagome lattice near 2/3-filling. Our main focus lies on the strongly anisotropic case in which the nearest–neighbor repulsions V and V ' are large compared to the hopping amplitudes | t | and | t '|. When t = t ' = 0, the system has a charge ordered insulating ground state where the charges align in striped configurations. Doping one electron or hole into the ground state yields an anisotropic metal at V ' > V , where the particle fractionalizes along the V '-bonds while propagates along the V -bonds in a one–body like manner. The sixth order ring exchange processes around the hexagonal unit of the lattice play a crucial role in forming a bound state of fractional charges.
Motivated by the recent discovery of metallic kagome lattice materials,
AV3Sb5 (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/t on narrower cylinders, including a metallic phase at
U<Uc1, two insulating intermediate phases (a translational symmetry breaking phase at
Uc1<U<Uc2 and a quantum spin liquid phase at
Uc2<U<Uc3), and the kagome antiferromagnetic phase at
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 whose nature is consistent with Slater's transition scenario. The magnetic phase transition between two insulating intermediate phases at
Uc2 is first order. Our findings may provide insights into exotic kagome lattice materials.
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.
A solvable model of d = 1 spinless fermions at half-filling which exhibits a Mott transition is studied in detail. Many response functions are computed: at zero and nonzero temperatures, in the insulating and metallic sites, at the transition, and at q ≃ 0, 2k F . Some quantities are computed exactly, others only upto a scale factor. Some results are old, but mentioned here for completeness. Some are rederived using new tools such as conformal invariance. The rest are new. Next, the effect of randomness on the Mott state is explored. It is found, on the basis of Imry-Ma type arguments that no matter how large the gap is, the Mott insulator turns into an Anderson insulator immediately.