The kagome Hubbard model (KHM) is a paradigmatic example of a frustrated two-dimensional model. While its strongly correlated regime, described by a Heisenberg model, is of topical interest due to its enigmatic prospective spin-liquid ground state, the weakly and moderately correlated regimes remain largely unexplored. Motivated by the rapidly growing number of metallic kagome materials (e.g., Mn$_3$Sn, Fe$_3$Sn$_2$, FeSn, Co$_3$Sn$_2$S$_2$, Gd$_3$Ru$_4$Al$_{12}$), we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory (DMFT), the dynamical vertex approximation (D$Γ$A), and determinant quantum Monte Carlo (DQMC). In contrast to the archetypal square-lattice, we find no tendencies towards magnetic ordering, as magnetic correlations remain short-range. Nevertheless, the magnetic correlations undergo a remarkable crossover as the system approaches the metal-to-insulator transition. The Mott transition itself does however not affect the magnetic correlations. Our equal-time and dynamical structure factors can be used as a reference for inelastic neutron scattering experiments on the growing family of metallic kagome materials.
Recent experimental discovery of several families of kagome-lattice materials has boosted the interest in electronic correlations on kagome lattice. As an initial step to understand the observed complex phenomena, it is helpful to know the correspondence between simple forms of interactions and the induced correlated states on kagome lattice. Considering the lack of such studies, here we systematically investigate the attractive kagome-lattice Hubbard model using the mean-field approach and determinant quantum Monte Carlo (DQMC). A charge-density-wave order satisfying the triangle rule is pred…
We respond to the comment arXiv:1809.03931 put forward by Li-Han Chen, Zhen Liu, and Jian-Tin Zheng on our work Kiesel, Platt, and Thomale, Phys. Rev. Lett. 110, 126405 (2013). All misunderstandings and misconceptions communicated in the comment are addressed in light of the status quo of functional renormalization group.
Motivated by the recent discovery of metallic kagome lattice materials, AV$_{3}$Sb$_{5}$ (A=K, Rb, Cs), we investigate the ground state of the half-filled kagome lattice Hubbard model by employing the density-matrix renormalization group (DMRG) method. We identify a metal-insulator transition around $U \thicksim U_{c1}$ and four distinct phases as a function of $U/t$ on narrower cylinders, including a metallic phase at $U < U_{c1}$, two insulating intermediate phases: a translational symmetry breaking phase at $U_{c1} < U < U_{c2}$ and a quantum spin liquid phase at $U_{c2} < U < U_{c3}$, and …
Unconventional ferromagnetism and superconductivity in the imbalanced kagome-lattice Hubbard model are investigated by the mean-field theory and determinant quantum Monte Carlo method. Due to the asymmetric band structure of kagome lattice, the spin-$z$ ferromagnetic order intrinsically exists in the system, which is first enhanced by the interaction, and then continuously destructed after reaching a maximum at a moderate interaction strength. In contrast, the $xy$-plane ferromagnetism develops only above a critical interaction, which is estimated to be $U_c/t=3.65 \pm 0.05$ by finite-size sca…
We study the symmetry properties of the single-band Hubbard model with general spin-orbit coupling (SOC) on the Kagome lattice. We show that the global U(1) spin-rotational symmetry is present in the Hubbard Hamiltonian owing to the inversion symmetry centered at sites. The corresponding spin Hamiltonian has, therefore, the SO(2) spin-rotational symmetry, which can be captured by including SOC non-perturbatively. The exact classical groundstates, which we obtain for arbitrary SOC, are governed by the SU(2) fluxes associated with SOC threading the constituent triangles. The groundstates break t…
The dominating superconducting pairing symmetry of the kagome-lattice Hubbard model is investigated using the determinant quantum Monte Carlo method. The superconducting instability occurs when doping the correlated insulators formed by the Hubbard interaction near the Dirac filling, and the superconducting state exhibits an electron-hole asymmetry. Among the pairing symmetries allowed, we demonstrate that the dominating channel is d-wave in the hole-doped case. This opens the possibility of condensation into an unconventional $d_{x^2-y^2}+id_{xy}$ phase, which is characterized by an integer t…
Mott transition in the Hubbard model on the hyper-kagome lattice
基于最近对Na $_4$ Ir $_3$ O $_8$化合物的实验研究，我们采用动力学集团近似（DCA）方法（$N_c$ =12）结合连续时间量子蒙特卡罗（CT QMC）方法研究了“超kagome晶格”上的哈伯德模型.当Hubbard相互作用$U/W$（$W$是带宽）超过$T$ =0.1时的值1.2时，系统经历Mott转变，并且由于磁关联和电子的动能之间的竞争（由于几何阻挫）而显示重入行为。我们观察到一个“临界减速”的双人入住，这表明一个连续的过渡的证据。最近邻和次最近邻自旋-自旋关联表明，在我们的数值工具可以访问的温度范围内的弱耦合制度和反铁磁（AF）莫特绝缘体在强耦合制度的顺磁金属态。
We study the Hubbard model with time-reversal invariant flux and spin-orbit coupling and position-dependent onsite energies on the kagome lattice, using numerical and analytical methods. In particular, we perform calculations using real space dynamical mean-field theory (R-DMFT). To study the topological properties of the system, we use the topological Hamiltonian approach. We obtain a rich phase diagram: for weak and intermediate interactions, depending on the model parameters, the system is in the band insulator, topological insulator, or metallic phase, while for strong interactions the sys…
Magnetic fluctuations near the Van Hove singularity in the kagome-lattice Hubbard model at finite doping
Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University（燕山大学理学院河北省微观结构材料物理重点实验室）；School of Physics and Astronomy, and Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学物理学系与教育部多尺度自旋物理重点实验室）
The Hubbard model on the kagome lattice is presently often considered as a minimal model to describe the rich low-temperature behavior of AV$_{3}$Sb$_{5}$ compounds (with A=K, Rb, Cs), including charge-density waves (CDWs), superconductivity, and possibly broken time-reversal symmetry. Here, we investigate, via variational Jastrow-Slater wave functions, the properties of its ground state when both onsite $U$ and nearest-neighbor $V$ Coulomb repulsions are considered at the van Hove filling. Our calculations reveal the presence of different interaction-driven CDWs and, contrary to previous reno…
We discuss the exact plaquette-ordered ground states of the generalized Hubbard model on the Kagomé lattice for several fillings, by constructing the Hamiltonian as a sum of products of projection operators for up and down spin sectors. The obtained exact ground states are interpreted as Néel ordered states on the bond-located electrons. We determine several parameter regions of the exact ground states, and calculate the entanglement entropy. We examine the above results by numerical calculations based on exact diagonalization and density-matrix renormalization group methods.
This is a comment on Phys. Rev. Lett. {\bf 110}, 126405 (2013), showing it biases the ferromagnetic order more than mean field theories would do. With over-biases like this, the theoretical method applied in the given context is called into question.
Superfluidity without charge order in the attractive Hubbard model on the kagome lattice
Beijing Computational Science Research Center（北京计算科学研究中心）；College of Physics and Electronic Engineering, Chongqing Normal University（重庆师范大学物理与电子工程学院）；Department of Physics, University of Houston（休斯顿大学物理系）；Texas Center for Superconductivity, University of Houston（休斯顿大学超导电性中心）
We explore magnetic behavior of kagome francisites Cu3Bi(SeO3)2O2X (X = Cl and Br) using first-principles calculations. To this end, we propose an approach based on the Hubbard model in the Wannier functions basis constructed on the level of local-density approximation (LDA). The ground-state spin configuration is determined by a Hartree-Fock solution of the Hubbard model both in zero magnetic field and in applied magnetic fields. Additionally, parameters of an effective spin Hamiltonian are obtained by taking into account the hybridization effects and spin-orbit coupling. We show that only th…
We use scanning tunneling microscopy/spectroscopy (STM/S) to elucidate the atomically resolved electronic structure in strongly correlated topological kagome magnet Mn$_3$Sn. In stark contrast to its broad single-particle electronic structure, we observe a pronounced resonance with a Fano line shape at the Fermi level resembling the many-body Kondo resonance. We find that this resonance does not arise from the step edges or atomic impurities, but the intrinsic kagome lattice. Moreover, the resonance is robust against the perturbation of a vector magnetic field, but broadens substantially with …
Interplay of magnetic and thermodynamic responses in the kagome-triangular system
Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）；School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学理学院）；Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University（燕山大学理学院河北省微观材料物理重点实验室）；Beijing Computational Science Research Center（北京计算科学研究中心）
Coexisting density-wave and superconducting states along with the large anomalous Hall effect in the absence of local magnetism remain intriguing and enigmatic features of the AV$_3$Sb$_5$ kagome metals (A = K, Rb, Cs). Here, we demonstrate via optical spectroscopy and density-functional calculations that low-energy dynamics of KV$_3$Sb$_5$ is characterized by unconventional localized carriers, which are strongly renormalized across the density-wave transition and indicative of electronic correlations. Strong phonon anomalies are prominent not only below the density-wave transition, but also a…
There has been a growing interest in realizing topologically nontrivial states of matter in band insulators, where a quantum Hall effect can appear as an intrinsic property of the band structure. While the on-going progress is under way with a number of directions, the possibility of realizing novel interaction-generated topological phases, without the requirement of a nontrivial invariant encoded in single-particle wavefunction or band structure, can significantly extend the class of topological materials and is thus of great importance. Here, we show an interaction-driven topological phase e…
Correlation-Induced Topological Reconstruction in a Periodically Driven Kagome Mott Insulator
National Institute of Science Education and Research（印度科学与教育国立研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国立中心）；Technische Universität Braunschweig（布伦瑞克工业大学）
Two-dimensional (2D) metal-organic frameworks (MOFs) in a kagome lattice can exhibit strong electron-electron interactions, which can lead to tunable quantum phases including many exotic magnetic phases. While technological developments of 2D MOFs typically take advantage of substrates for growth, support, and electrical contacts, investigations often ignore substrates and their dramatic influence on electronic properties of MOFs. Here, we show how substrates alter the correlated magnetic phases in kagome MOFs using systematic density functional theory and mean-field Hubbard calculations. We d…
The kagome lattice, whose electronic valence band (VB) structure includes two Dirac bands and one flat band, offers a rich space to realise tuneable topological and strongly correlated electronic phases in two-dimensional (2D) and layered materials. While strong electron correlations have been observed in inorganic kagome crystals, they remain elusive in organic systems. The latter offer versatile synthesis protocols via molecular self-assembly and metal-ligand coordination. Here, we report the synthesis of a 2D metal-organic framework (MOF) where di-cyano-anthracene (DCA) molecules form a kag…
There have been extensive recent developments on kagome metals, such as T$_m$X$_n$ (T= Fe, Co and X= Sn, Ge) and $A$V$_3$Sb$_5$ ($A=$ Cs, K, Rb). An emerging issue is the nature of correlated phases when topologically \textit{non-trivial} bands cross the Fermi level. Here, we consider an extended Hubbard model on the kagome lattice in the presence of spin-orbit couplings, involving a Kramer's pair of bands that have opposite Chern numbers and are isolated in the band structure. We construct an effective model in a time-reversal (T) symmetric lattice description. We determine the correlated pha…
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. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. The nature of charge excitations in cluster Mott insulators can be quite different from co…
We theoretically study a generalized Hubbard model on moiré superlattices of twisted bilayers, and find very rich filling-factor-dependent quantum phase diagrams tuned by interaction strength and twist angle. Strong long-range Coulomb interaction in the moiré-Hubbard model induces Wigner crystals at a series of fractional filling factors. The effective lattice of the Wigner crystal is controlled by the filling factor, and can be triangle, rectangle, honeycomb, kagome, etc, providing a single platform to realize many different spin models on various lattices by simply tuning carrier density. In…
Structural and magnetic properties of the geometrically frustrated layered compound YBaCo4O7 have been studied by magnetization and neutron diffraction. A layered type crystal structure, with alternating tetrahedral layers of Kagomé and triangular types, along the c axis (hexagonal symmetry, space group P63mc) has been found. The oxygen content of the present compound was determined by iodometric titration to be 7.00{\pm}0.01. Presence of a short-range antiferromagnetic ordering (below TN ~ 110 K) has been concluded from the appearance of an addition broad magnetic peak (at Q ~ 1.35 Å-1) in th…
