Taking cue from the recent experimental realization of metallic phases in Kagome materials we report the low temperature signatures and thermal scales of Kagome metals and insulators, determined in the framework of the Kagome Hubbard model, using a non perturbative numerical approach. In contrast to the existing consensus we establish a flat band localized insulator in the weak coupling regime which crosses over to a non Fermi liquid (NFL) metal at intermediate coupling, followed by a first order metal-Mott insulator transition in the strong coupling regime. We provide the first accurate estimates of the thermal scales of this model and analyze the NFL phases in terms of resilient quasiparticles and short range magnetic correlations. With our unprecedented access to the low temperature phases and sufficiently large system sizes, we provide the essential benchmarks for the prospective experiments on the Kagome metal and insulators in terms of their thermodynamic, spectroscopic and transport signatures.
Kagome metals exhibit a rich interplay of topology, electronic correlations, and lattice dynamics. Recent discoveries of Kagome materials with a flat band near the Fermi level have revealed a variety of correlated electronic phases. However, elucidating their microscopic origin remains challenging, as realistic descriptions require accounting for multiple orbitals and competing interactions on an equal footing. To disentangle correlation effects from material-specific details and identify the essential physics of the flat-band regime, we study the single-orbital Kagome-Hubbard model at flat-band fillings using dynamical mean-field theory. We find strong signatures of flat-band ferromagnetism, consistent with exact and mean-field ground-state results. Moreover, we uncover an unconventional quasi-ordered phase in which a partially filled spin-polarized flat band pinned at the Fermi level gives rise to persistent local spin fluctuations down to zero temperature, in striking contrast to the classical behavior expected for a conventional ferromagnet. Our results demonstrate that these anomalous fluctuations are an intrinsic consequence of the flat-band degeneracy and establish a minimal framework for understanding correlation effects in flat-band Kagome systems.
Most Mott systems display a low-temperature phase coexistence region around the metal-insulator transition. The domain walls separating the respective phases have very recently been observed displaying unusual properties both in simulations and in experiments. First, they often cover a significant volume fraction, thus cannot be neglected. Second, they resemble neither a typical metal nor a standard insulator, displaying unfamiliar temperature dependence of (local) transport properties. Here we take a closer look at such domain wall matter by examining an appropriate unstable solution of the Hubbard model. We show that transport in this regime is dominated by the emergence of ``resilient quasiparticles'' displaying strong non-Fermi liquid features, reflecting the quantum-critical fluctuations in the vicinity of the Mott point.
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.
Flat-band systems provide a promising platform for exploring exotic correlated phases owing to quenched kinetic energy and enhanced interaction effects. In this work, we investigate the flat-band superfluid transition in the attractive kagome Hubbard model using large-scale determinant quantum Monte Carlo simulations accelerated by fast Fourier transforms and delay updates. Through systematic calculations of the transition temperature, spin susceptibility, and density compressibility, we establish the finite-temperature phase diagram at the flat-band filling
ρ=5/3 and find a clear linear scaling of the superfluid transition temperature with the interaction strength,
Tc=0.0314∣U∣. Our results reveal a wide separation of temperature scales between local pair formation and global phase coherence, which stabilizes a broad intermediate supercompressible bosonic fluid region of preformed pairs that bridges the normal Fermi gas and the flat-band superfluid. We further demonstrate that both the transition temperature and density compressibility are significantly enhanced in the flat band compared to van Hove fillings. Our findings highlight the essential role of flat-band-enhanced pair-density fluctuations in separating the pairing and phase-coherence scales, offering clear experimental signatures for probing flat-band superfluidity and superconductivity in cold-atom and kagome-material platforms.
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.
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.