arXiv:1201.0654 · Physical Review Letters

Kondo Metal and Ferrimagnetic Insulator on the Triangular Kagome Lattice

Yao‐Hua Chen, Hong-Shuai Tao, Dao‐Xin Yao, Wu-Ming Liu

Published Jun 13, 2012• 107 citations

Abstract

We obtain the rich phase diagrams in the Hubbard model on the triangular kagome lattice as a function of interaction, temperature, and asymmetry by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. The phase diagrams show the asymmetry separates the critical points in the Mott transition of two sublattices on the triangular kagome lattice and produces two novel phases called plaquette insulator with a clearly visible gap and a gapless Kondo metal. When the Coulomb interaction is stronger than the critical value U(c), a short range paramagnetic insulating state, which is a candidate for the short rang resonating valence-bond spin liquid, emerges before the ferrimagnetic order is formed independent of asymmetry. Furthermore, we discuss how to measure these phases in future experiments.

DOI: 10.1103/physrevlett.108.246402

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arXiv:1201.0654 · Physical Review Letters

Kondo Metal and Ferrimagnetic Insulator on the Triangular Kagome Lattice

Yao‐Hua Chen, Hong-Shuai Tao, Dao‐Xin Yao, Wu-Ming Liu

Published Jun 13, 2012• 107 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.108.246402

Related papers

Exotic phase diagram of a cluster charging model of bosons on the kagome lattice

Sergei V. Isakov, Arun Paramekanti, Yong Baek Kim

We study a model of hard-core bosons on the kagome lattice with short-range hopping $(t)$ and repulsive interactions $(V)$ . This model directly maps onto an easy-axis $S=1∕2$ XXZ model on the kagome lattice and is also related, at large $V∕t$ , 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 $T=0$ , we show that this model exhibits a superfluid phase at small $V∕t$ and an insulating phase at large $V∕t$ , separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at $T=0$ 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 ${Z}_{2}$ 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 $V<{V}_{c}$ . We find that this is a Kosterlitz-Thouless transition at small $V∕t$ but changes to a first order transition for $V$ closer to ${V}_{c}$ . We argue that this first order thermal transition is consistent with the presence of a nearby ${Z}_{2}$ insulating ground state obtained from the superfluid ground state by condensing double vortices.We study a model of hard-core bosons on the kagome lattice with short-range hopping $(t)$ and repulsive interactions $(V)$. This model directly maps onto an easy-axis $S=1∕2$ XXZ model on the kagome lattice and is also related, at large $V∕t$, 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 $T=0$, we show that this model exhibits a superfluid phase at small $V∕t$ and an insulating phase at large $V∕t$, separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at $T=0$ 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 ${Z}_{2}$ 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 $V<{V}_{c}$. We find that this is a Kosterlitz-Thouless transition at small $V∕t$ but changes to a first order transition for $V$ closer to ${V}_{c}$. We argue that this first order thermal transition is consistent with the presence of a nearby ${Z}_{2}$ insulating ground state obtained from the superfluid ground state by condensing double vortices.

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We study the ground-state phase diagram of the spin- $1/2$ antiferromagnetic Heisenberg model on the square-kagome lattice using infinite projected entangled-pair states (iPEPS). By systematically varying the ratio of exchange couplings on triangular and square plaquettes, we establish a complete quantum phase diagram in the thermodynamic limit. In the intermediate-coupling regime, we identify four distinct nonmagnetic phases that are unambiguously characterized as valence-bond crystals (VBCs) by their symmetry-inequivalent patterns of strong and weak spin-spin correlations. These include a plaquette crossed-dimer VBC, a loop-six VBC stabilized around the isotropic point, a generalized pinwheel VBC with reduced rotational symmetry, and a decorated loop-six VBC proximate to ferrimagnetic order. We determine the phase boundaries using a combination of bond-resolved correlation functions, entanglement entropy, and magnetization. For transitions not accompanied by sharp entanglement signatures, we extract the spin gap from finite-field simulations, allowing us to distinguish gapped and gapless VBC phases. At larger coupling ratios, the system undergoes transitions into imperfect and perfect ferrimagnetic states. Our results resolve long-standing ambiguities in the square-kagome Heisenberg model and provide a quantitatively reliable reference for future theoretical and experimental studies of frustrated quantum magnets.We study the ground-state phase diagram of the spin-$1/2$ antiferromagnetic Heisenberg model on the square-kagome lattice using infinite projected entangled-pair states (iPEPS). By systematically varying the ratio of exchange couplings on triangular and square plaquettes, we establish a complete quantum phase diagram in the thermodynamic limit. In the intermediate-coupling regime, we identify four distinct nonmagnetic phases that are unambiguously characterized as valence-bond crystals (VBCs) by their symmetry-inequivalent patterns of strong and weak spin-spin correlations. These include a plaquette crossed-dimer VBC, a loop-six VBC stabilized around the isotropic point, a generalized pinwheel VBC with reduced rotational symmetry, and a decorated loop-six VBC proximate to ferrimagnetic order. We determine the phase boundaries using a combination of bond-resolved correlation functions, entanglement entropy, and magnetization. For transitions not accompanied by sharp entanglement signatures, we extract the spin gap from finite-field simulations, allowing us to distinguish gapped and gapless VBC phases. At larger coupling ratios, the system undergoes transitions into imperfect and perfect ferrimagnetic states. Our results resolve long-standing ambiguities in the square-kagome Heisenberg model and provide a quantitatively reliable reference for future theoretical and experimental studies of frustrated quantum magnets.

arXiv:2503.07689Physical review. B./Physical review. BMar 10, 20261 citation

We study a model of hard-core bosons on the kagome lattice with short-range hopping

(t)

and repulsive interactions

(V)

. This model directly maps onto an easy-axis

S=1∕2

XXZ model on the kagome lattice and is also related, at large

V∕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=0

, we show that this model exhibits a superfluid phase at small

V∕t

and an insulating phase at large

V∕t

, separated by a continuous quantum phase transition at ${V}_{c}∕t\ensuremath{\approx}19.8$. The insulating phase at

T=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

{Z}_{2}

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<{V}_{c}

. We find that this is a Kosterlitz-Thouless transition at small

V∕t

but changes to a first order transition for

V

closer to

{V}_{c}

. We argue that this first order thermal transition is consistent with the presence of a nearby

{Z}_{2}

insulating ground state obtained from the superfluid ground state by condensing double vortices.

We study the ground-state phase diagram of the spin-

1/2

antiferromagnetic Heisenberg model on the square-kagome lattice using infinite projected entangled-pair states (iPEPS). By systematically varying the ratio of exchange couplings on triangular and square plaquettes, we establish a complete quantum phase diagram in the thermodynamic limit. In the intermediate-coupling regime, we identify four distinct nonmagnetic phases that are unambiguously characterized as valence-bond crystals (VBCs) by their symmetry-inequivalent patterns of strong and weak spin-spin correlations. These include a plaquette crossed-dimer VBC, a loop-six VBC stabilized around the isotropic point, a generalized pinwheel VBC with reduced rotational symmetry, and a decorated loop-six VBC proximate to ferrimagnetic order. We determine the phase boundaries using a combination of bond-resolved correlation functions, entanglement entropy, and magnetization. For transitions not accompanied by sharp entanglement signatures, we extract the spin gap from finite-field simulations, allowing us to distinguish gapped and gapless VBC phases. At larger coupling ratios, the system undergoes transitions into imperfect and perfect ferrimagnetic states. Our results resolve long-standing ambiguities in the square-kagome Heisenberg model and provide a quantitatively reliable reference for future theoretical and experimental studies of frustrated quantum magnets.