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:1402.6612 · Physical Review B

Kagome lattice Hubbard model at half filling

Siegfried Guertler

Published Aug 8, 2014• 14 citations
arXivHTMLPDF

Abstract

We investigate the kagome lattice Hubbard model at half filling using the variational Monte Carlo method by testing the $U(1)$-Dirac spin-liquid, uniform, and valence bond crystal states. Even for the large-$U$ case, the $U(1)$ Dirac state, which is the optimal state in the Heisenberg model, cannot be recovered. While the finite-$U$ Hubbard model allows for the introduction of vacancies in a different manner compared to the $t\text{\ensuremath{-}}J$ model, the physics appears to have many similarities. In particular, a valence bond crystal is formed in the intermediate-$U$ regime. We observe an impact of the formation of this valence bond crystal on a possible Mott transition in this model and discuss the properties of the wave function.

DOI
10.1103/physrevb.90.081105

Related papers

Valence-bond crystal in the extended kagome spin- 1 2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach

Yasir Iqbal, Federico Becca, Didier Poilblanc

The highly frustrated spin-$\frac{1}{2}$ quantum Heisenberg model with both nearest (${J}_{1}$) and next-nearest (${J}_{2}$) neighbor exchange interactions is revisited by using an extended variational space of projected wave functions that are optimized with state-of-the-art methods. Competition between modulated valence-bond crystals (VBCs) proposed in the literature and the Dirac spin liquid (DSL) is investigated. We find that the addition of a small ferromagnetic next-nearest-neighbor exchange coupling $|{J}_{2}|>0.09{J}_{1}$ leads to stabilization of a 36-site unit cell VBC, although the DSL remains a local minimum of the variational parameter landscape. This implies that the VBC is not trivially connected to the DSL; instead it possesses a nontrivial flux pattern and large dimerization.

arXiv:1011.3954•Physical Review B•Mar 7, 2011•85 citations

Doping on the kagome lattice: A variational Monte Carlo study of the t - J model

Siegfried Guertler, H. Monien

We study doping on the kagome lattice by exploring the $t$-$J$ model with variational Monte-Carlo. We use a number of Gutzwiller projected spin-liquid and valence-bond-crystal states and compare their energies at several system sizes. We find that introducing mobile holes drives the system away from the spin-liquid state proposed by Ran et al. [Y. Ran, M. Hermele, P. A. Lee, and X. G. Wen, Phys. Rev. Lett. 98, 117205 (2007)] for the undoped system, toward a uniform state with zero flux. On top of the uniform state a valence-bond crystal of the Hastings type is formed for low doping. The results are compared and agree well with exact diagonalization on small clusters.

arXiv:1105.0581•Physical Review B•Nov 10, 2011•14 citations

Valence-bond crystals in the kagomé spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study

Yasir Iqbal, Federico Becca, Didier Poilblanc

In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagomé lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwiller-projected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. | J 2 | ≈ 0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.

arXiv:1203.3421•New Journal of Physics•Nov 28, 2012•40 citations

Bond formation effects on the metal-insulator transition in the half-filled kagome Hubbard model

亮太 比嘉, Kenichi Asano

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 $S=1/2$ 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 $S=1/2$ spins, which are consistent with the ground states of the Kagome antiferromagnet.

Physical review. B./Physical review. B•Jun 9, 2016•12 citations

Spin-phonon interactions on the kagome lattice: Dirac spin liquid versus valence-bond solids

Francesco Ferrari, Federico Becca, Roser Valentí

We investigate the impact of spin-phonon coupling on the $S=1/2$ Heisenberg model on the kagome lattice. For the pure spin model, there is increasing evidence that the low-energy properties can be correctly described by a Dirac spin liquid, in which spinons with a conical dispersion are coupled to emergent gauge fields. Within this scenario, the ground-state wave function is well approximated by a Gutzwiller-projected fermionic state [Ran, Hermele, Lee, and Wen, Phys. Rev. Lett. 98, 117205 (2007)]. However, the existence of $U(1)$ gauge fields may naturally lead to instabilities when small perturbations are included. Phonons are ubiquitous in real materials and may play a relevant role in the determination of the actual physical properties of the kagome antiferromagnet. Therefore, we perform a step forward in this direction, including phonon degrees of freedom (at the quantum level) and applying a variational approach based upon Gutzwiller-projected fermionic Ans\"atze. Our results suggest that the Dirac spin liquid is stable for small spin-phonon couplings, while valence-bond solids are obtained at large couplings. Even though different distortions can be induced by the spin-phonon interaction, the general aspect is that the energy is lowered by maximizing the density of perfect hexagons in the dimerization pattern.

arXiv:2311.09823•Physical review. B./Physical review. B•Apr 17, 2024•8 citations

Global phase diagram of doped quantum spin liquid on the Kagome lattice

Zheng-Tao Xu, Zheng‐Cheng Gu, Shuo Yang

It has long been believed that doped quantum spin liquids (QSLs) can give rise to fascinating quantum phases, including the possibility of high-temperature superconductivity (SC) as proposed by P. W. Anderson's resonating valence bond (RVB) scenario. The Kagome lattice $t$-$J$ model is known to exhibit spin liquid behavior at half-filling, making it an ideal system for studying the properties of doped QSL. In this study, we employ the fermionic projected entangled simplex state (PESS) method to investigate the ground state properties of the Kagome lattice $t$-$J$ model with $t/J = 3.0$. Our results reveal a phase transition from charge density wave (CDW) states to uniform states around a critical doping level $δ_c \approx 0.27$. Within the CDW phase, we observe different types of Wigner crystal (WC) formulated by doped holes that are energetically favored. As we enter the uniform phase, a non-Fermi liquid (NFL) state emerges within the doping range $0.27 < δ< 0.32$, characterized by an exponential decay of all correlation functions. With further hole doping, we discover the appearance of a pair density wave (PDW) state within a narrow doping region $0.32 < δ< 1/3$. We also discuss the potential experimental implications of our findings.

arXiv:2404.05685•Apr 8, 2024•0 citations
We investigate the kagome lattice Hubbard model at half filling using the variational Monte Carlo method by testing the U(1)U(1)U(1)-Dirac spin-liquid, uniform, and valence bond crystal states. Even for the large-UUU case, the U(1)U(1)U(1) Dirac state, which is the optimal state in the Heisenberg model, cannot be recovered. While the finite-UUU Hubbard model allows for the introduction of vacancies in a different manner compared to the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model, the physics appears to have many similarities. In particular, a valence bond crystal is formed in the intermediate-UUU regime. We observe an impact of the formation of this valence bond crystal on a possible Mott transition in this model and discuss the properties of the wave function.
The highly frustrated spin-12\frac{1}{2}21​ quantum Heisenberg model with both nearest (J1{J}_{1}J1​) and next-nearest (J2{J}_{2}J2​) neighbor exchange interactions is revisited by using an extended variational space of projected wave functions that are optimized with state-of-the-art methods. Competition between modulated valence-bond crystals (VBCs) proposed in the literature and the Dirac spin liquid (DSL) is investigated. We find that the addition of a small ferromagnetic next-nearest-neighbor exchange coupling ∣J2∣>0.09J1|{J}_{2}|>0.09{J}_{1}∣J2​∣>0.09J1​ leads to stabilization of a 36-site unit cell VBC, although the DSL remains a local minimum of the variational parameter landscape. This implies that the VBC is not trivially connected to the DSL; instead it possesses a nontrivial flux pattern and large dimerization.
We study doping on the kagome lattice by exploring the ttt-JJJ model with variational Monte-Carlo. We use a number of Gutzwiller projected spin-liquid and valence-bond-crystal states and compare their energies at several system sizes. We find that introducing mobile holes drives the system away from the spin-liquid state proposed by Ran et al. [Y. Ran, M. Hermele, P. A. Lee, and X. G. Wen, Phys. Rev. Lett. 98, 117205 (2007)] for the undoped system, toward a uniform state with zero flux. On top of the uniform state a valence-bond crystal of the Hastings type is formed for low doping. The results are compared and agree well with exact diagonalization on small clusters.
In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagomé lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwiller-projected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. | J 2 | ≈ 0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.
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 investigate the impact of spin-phonon coupling on the S=1/2S=1/2S=1/2 Heisenberg model on the kagome lattice. For the pure spin model, there is increasing evidence that the low-energy properties can be correctly described by a Dirac spin liquid, in which spinons with a conical dispersion are coupled to emergent gauge fields. Within this scenario, the ground-state wave function is well approximated by a Gutzwiller-projected fermionic state [Ran, Hermele, Lee, and Wen, Phys. Rev. Lett. 98, 117205 (2007)]. However, the existence of U(1)U(1)U(1) gauge fields may naturally lead to instabilities when small perturbations are included. Phonons are ubiquitous in real materials and may play a relevant role in the determination of the actual physical properties of the kagome antiferromagnet. Therefore, we perform a step forward in this direction, including phonon degrees of freedom (at the quantum level) and applying a variational approach based upon Gutzwiller-projected fermionic Ans\"atze. Our results suggest that the Dirac spin liquid is stable for small spin-phonon couplings, while valence-bond solids are obtained at large couplings. Even though different distortions can be induced by the spin-phonon interaction, the general aspect is that the energy is lowered by maximizing the density of perfect hexagons in the dimerization pattern.
It has long been believed that doped quantum spin liquids (QSLs) can give rise to fascinating quantum phases, including the possibility of high-temperature superconductivity (SC) as proposed by P. W. Anderson's resonating valence bond (RVB) scenario. The Kagome lattice ttt-JJJ model is known to exhibit spin liquid behavior at half-filling, making it an ideal system for studying the properties of doped QSL. In this study, we employ the fermionic projected entangled simplex state (PESS) method to investigate the ground state properties of the Kagome lattice ttt-JJJ model with t/J=3.0t/J = 3.0t/J=3.0. Our results reveal a phase transition from charge density wave (CDW) states to uniform states around a critical doping level δc≈0.27δ_c \approx 0.27δc​≈0.27. Within the CDW phase, we observe different types of Wigner crystal (WC) formulated by doped holes that are energetically favored. As we enter the uniform phase, a non-Fermi liquid (NFL) state emerges within the doping range 0.27<δ<0.320.27 < δ< 0.320.27<δ<0.32, characterized by an exponential decay of all correlation functions. With further hole doping, we discover the appearance of a pair density wave (PDW) state within a narrow doping region 0.32<δ<1/30.32 < δ< 1/30.32<δ<1/3. We also discuss the potential experimental implications of our findings.