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arXiv:2105.00450 · Physical review. B./Physical review. B

Metal-insulator transition and intermediate phases in the kagome lattice Hubbard model

Rong-Yang Sun, Zheng Zhu

Published Sep 29, 2021• 21 citations
arXivHTMLPDF

Abstract

Motivated by the recent discovery of metallic kagome lattice materials, ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ (A = K, Rb, Cs), we investigate the ground state of the half-filled kagome lattice Hubbard model by employing the density-matrix renormalization group 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 $U<{U}_{c1}$, 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 the kagome antiferromagnetic phase at $U>{U}_{c3}$. 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 ${U}_{c1}$ whose nature is consistent with Slater's transition scenario. The magnetic phase transition between two insulating intermediate phases at ${U}_{c2}$ is first order. Our findings may provide insights into exotic kagome lattice materials.

DOI
10.1103/physrevb.104.l121118

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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∼Uc1U\ensuremath{\sim}{U}_{c1}U\ensuremath∼Uc1​ 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.
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.
Two-dimensional density-matrix renormalization group method is employed to examine the ground-state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction UUU at ${U}_{\mathrm{c}1}\ensuremath{\sim}7.8t$ and ${U}_{\mathrm{c}2}\ensuremath{\sim}9.9t$ (ttt being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for $0\ensuremath{\le}U<{U}_{\mathrm{c}1}$ implies a metallic phase in this regime. For U>Uc2U>{U}_{\mathrm{c}2}U>Uc2​, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the ${120}^{\ensuremath{\circ}}$ N\'eel-ordered state realized in the limit of $U\ensuremath{\rightarrow}\ensuremath{\infty}$. For Uc1<U<Uc2{U}_{\mathrm{c}1}<U<{U}_{\mathrm{c}2}Uc1​<U<Uc2​, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K\mathrm{K}K and ${\mathrm{K}}^{\ensuremath{'}}$ points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing UUU and thus the superconductivity is unlikely in the intermediate phase.
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 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 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 study a model of hard-core bosons on the kagome lattice with short-range hopping (t)(t)(t) and repulsive interactions (V)(V)(V). This model directly maps onto an easy-axis S=1∕2S=1∕2S=1∕2 XXZ model on the kagome lattice and is also related, at large V∕tV∕tV∕t, to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo numerics, we map out the phase diagram of this model at half-filling. At T=0T=0T=0, we show that this model exhibits a superfluid phase at small V∕tV∕tV∕t and an insulating phase at large V∕tV∕tV∕t, separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at T=0T=0T=0 appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a ``spin liquid'' in magnetic language). We characterize this insulating phase as a uniform Z2{Z}_{2}Z2​ fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for V<VcV<{V}_{c}V<Vc​. We find that this is a Kosterlitz-Thouless transition at small V∕tV∕tV∕t but changes to a first order transition for VVV closer to Vc{V}_{c}Vc​. We argue that this first order thermal transition is consistent with the presence of a nearby Z2{Z}_{2}Z2​ insulating ground state obtained from the superfluid ground state by condensing double vortices.