Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.01396 · Physical review. B./Physical review. B

Cluster Mott insulators and two Curie-Weiss regimes on an anisotropic kagome lattice

Gang Chen, Hae‐Young Kee, Yong Baek Kim

Published Jun 15, 2016• 47 citations
arXivHTMLPDF

Abstract

Motivated by recent experiments on the quantum-spin-liquid candidate material ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, we study a single-band extended Hubbard model on an anisotropic kagome lattice with the $\frac{1}{6}$ electron filling. Due to the partial filling of the lattice, the intersite 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 conventional Mott insulator and we show that there exists a cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only $\frac{1}{3}$ of the total spinon excitations are magnetically active. Based on these results, we propose that the two Curie-Weiss regimes of the spin susceptibility in ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.

DOI
10.1103/physrevb.93.245134

Related papers

Spin susceptibility anomaly in cluster Mott insulators on a partially-filled anisotropic Kagome lattice: applications to LiZn2Mo3O8

Gang Chen, Hae‐Young Kee, Yong Baek Kim

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. We provide examples of such cluster Mott insulators and study the phase transitions between metallic states and cluster Mott insulators on an anisotropic Kagome lattice. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. However, the nature of charge excitations in different cluster Mott insulators could be quite different and we show that there exists a novel cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 1/3 of the total spinon excitations are magnetically active. The strong coupling limit of the same model is also analyzed via a Kugel-Khomskii-like model. Based on these results, we propose that the anomalous behavior of the finite-temperature spin-susceptibility in LiZn2Mo3O8 may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.

arXiv:1408.1963•Aug 8, 2014•1 citation

Emergent orbitals in the cluster Mott insulator on a breathing kagome lattice

Gang Chen, Patrick A. Lee

Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the intersite charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3, as observed in ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$. Furthermore, at low temperatures, each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin-liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ are discussed, including an argument that the charge ordering must be short ranged if the charge per Mo is slightly off stoichiometric.

arXiv:1709.09789•Physical review. B./Physical review. B•Jan 12, 2018•36 citations

Beyond a cluster-Mott state in the breathing kagome lattice of LiZn 2 Mo 3 O 8

Sergey V Streltsov, Daisuke Takegami, Ryo Nakamura +10 more

Searching of materials, where a long-range magnetic order is suppressed by quantum fluctuations and a quantum spin liquid state realizes, is one of the central problems in the modern condensed matter physics. A possible candidate for such a state on the breathing Kagome lattice ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ is scrutinized by hard x-ray photoemission spectroscopy (HAXPES), cluster dynamical mean-field theory (cDMFT), and exact diagonalization of an extended Hubbard model. The Mo $3d$ core level HAXPES peaks of ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ are accompanied by shoulders on their lower energy side which are absent in ${\mathrm{Zn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$. The shoulder peaks observed only in ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ indicate ${\mathrm{Mo}}^{3+}$ and ${\mathrm{Mo}}^{4+}$ charge fluctuations. The cDMFT calculations not only describe experimental valence-band HAXPES spectra demonstrating importance of the correlation effects, but also feature nonlocal spin fluctuations. Exact diagonalization taking into account intertrimer Coulomb repulsion demonstrates long-range charge fluctuations consistent with HAXPES results.

Physical review. B./Physical review. B•Feb 11, 2025•2 citations

Fractionalized Charge Excitations in a Spin Liquid on Partially Filled Pyrochlore Lattices

Gang Chen, Hae‐Young Kee, Yong Baek Kim

We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems [corrected]. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in x-ray scattering experiments. Various other experimental signatures of the exotic cluster Mott insulator are discussed in light of candidate materials with partially filled bands on the pyrochlore lattice.

arXiv:1402.5425•Physical Review Letters•Nov 7, 2014•26 citations

Spectroscopic Evidence for Possible Quantum Spin Liquid Behavior in a Two-Dimensional Mott Insulator

Haiyang Chen, Fo-Hong Wang, Qiang Gao +6 more

Mott insulators with localized magnetic moments will exhibit a quantum spin liquid state when the quantum fluctuations are strong enough to suppress the ordering of the spins. Such an entangled state will give rise to collective excitations, in which spin and charge information are carried separately. Our angle-resolved photoemission spectroscopy measurements on single-layer 1T-TaS_{2} show a flat band around the zone center and a gap opening of about 200 meV in the low temperature, indicating 2D Mott insulating nature in the system. This flat band is dispersionless in momentum space but shows anomalously broad width around the zone center and the spectral weight decays rapidly as momentum increases. The observation is described as a spectral continuum from electron fractionalization, corroborated by a low energy effective model. The intensity of the flat band is reduced by surface doping with magnetic adatoms and the gap is closing, a result from the interaction between spin impurities coupled with spinons and the chargons, which gives rise to a charge redistribution. Doping with nonmagnetic impurities behaves differently as the chemical potential shift dominates. These findings provide insight into the quantum spin liquid states of strongly correlated electrons on 2D triangular lattices.

arXiv:2504.11778•Physical Review Letters•Feb 14, 2025•10 citations

Tripartite entangled plaquette state in a cluster magnet

Juan Carrasquilla, Gang Chen, Roger G. Melko

Using large-scale quantum Monte Carlo simulations we show that a spin-$\frac{1}{2}\phantom{\rule{1em}{0ex}}XXZ$ model on a two-dimensional anisotropic kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break $U(1)$ and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the spin liquid candidate ${\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, as well as a model of strongly correlated bosonic atoms loaded onto highly tunable trimerized optical kagome lattices.

arXiv:1704.03478•Physical review. B./Physical review. B•Aug 4, 2017•17 citations
Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, we study a single-band extended Hubbard model on an anisotropic kagome lattice with the 16\frac{1}{6}61​ electron filling. Due to the partial filling of the lattice, the intersite 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 conventional Mott insulator and we show that there exists a cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 13\frac{1}{3}31​ of the total spinon excitations are magnetically active. Based on these results, we propose that the two Curie-Weiss regimes of the spin susceptibility in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.
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. We provide examples of such cluster Mott insulators and study the phase transitions between metallic states and cluster Mott insulators on an anisotropic Kagome lattice. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. However, the nature of charge excitations in different cluster Mott insulators could be quite different and we show that there exists a novel cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 1/3 of the total spinon excitations are magnetically active. The strong coupling limit of the same model is also analyzed via a Kugel-Khomskii-like model. Based on these results, we propose that the anomalous behavior of the finite-temperature spin-susceptibility in LiZn2Mo3O8 may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.
Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the intersite charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3, as observed in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​. Furthermore, at low temperatures, each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin-liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ are discussed, including an argument that the charge ordering must be short ranged if the charge per Mo is slightly off stoichiometric.
Searching of materials, where a long-range magnetic order is suppressed by quantum fluctuations and a quantum spin liquid state realizes, is one of the central problems in the modern condensed matter physics. A possible candidate for such a state on the breathing Kagome lattice LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ is scrutinized by hard x-ray photoemission spectroscopy (HAXPES), cluster dynamical mean-field theory (cDMFT), and exact diagonalization of an extended Hubbard model. The Mo 3d3d3d core level HAXPES peaks of LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ are accompanied by shoulders on their lower energy side which are absent in Zn2Mo3O8{\mathrm{Zn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}Zn2​Mo3​O8​. The shoulder peaks observed only in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ indicate Mo3+{\mathrm{Mo}}^{3+}Mo3+ and Mo4+{\mathrm{Mo}}^{4+}Mo4+ charge fluctuations. The cDMFT calculations not only describe experimental valence-band HAXPES spectra demonstrating importance of the correlation effects, but also feature nonlocal spin fluctuations. Exact diagonalization taking into account intertrimer Coulomb repulsion demonstrates long-range charge fluctuations consistent with HAXPES results.
We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems [corrected]. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in x-ray scattering experiments. Various other experimental signatures of the exotic cluster Mott insulator are discussed in light of candidate materials with partially filled bands on the pyrochlore lattice.
Mott insulators with localized magnetic moments will exhibit a quantum spin liquid state when the quantum fluctuations are strong enough to suppress the ordering of the spins. Such an entangled state will give rise to collective excitations, in which spin and charge information are carried separately. Our angle-resolved photoemission spectroscopy measurements on single-layer 1T-TaS_{2} show a flat band around the zone center and a gap opening of about 200 meV in the low temperature, indicating 2D Mott insulating nature in the system. This flat band is dispersionless in momentum space but shows anomalously broad width around the zone center and the spectral weight decays rapidly as momentum increases. The observation is described as a spectral continuum from electron fractionalization, corroborated by a low energy effective model. The intensity of the flat band is reduced by surface doping with magnetic adatoms and the gap is closing, a result from the interaction between spin impurities coupled with spinons and the chargons, which gives rise to a charge redistribution. Doping with nonmagnetic impurities behaves differently as the chemical potential shift dominates. These findings provide insight into the quantum spin liquid states of strongly correlated electrons on 2D triangular lattices.
Using large-scale quantum Monte Carlo simulations we show that a spin-12XXZ\frac{1}{2}\phantom{\rule{1em}{0ex}}XXZ21​XXZ model on a two-dimensional anisotropic kagome lattice exhibits a tripartite entangled plaquette state that preserves all of the Hamiltonian symmetries. It is connected via phase boundaries to a ferromagnet and a valence-bond solid that break U(1)U(1)U(1) and lattice translation symmetries, respectively. We study the phase diagram of the model in detail, in particular the transitions to the tripartite entangled plaquette state, which are consistent with conventional order-disorder transitions. Our results can be interpreted as a description of the charge sector dynamics of a Hubbard model applied to the spin liquid candidate LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, as well as a model of strongly correlated bosonic atoms loaded onto highly tunable trimerized optical kagome lattices.