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:1302.0155 · Physical Review Letters

Unveiling the Physics of the Doped Phase of the t−J Model on the Kagome Lattice

Siegfried Guertler, H. Monien

Published Aug 27, 2013• 12 citations
arXivHTMLPDF

Abstract

We investigate the ground state properties of the kagome lattice t - J model at low doping by variational Monte Carlo calculations. The resulting state possesses an interesting balance of spin exchange and kinetic exchange through the building blocks of stars which are linked by triangles and their internal hexagons. While the spin exchange is taking place mainly on the stars, hopping is favored on the hexagons. There is a density modulation, resulting in the holes having an effective static contribution. From this observation, how holes lead to dimerization in this model and why a particular valence bond crystal pattern is formed can be understood. Furthermore, we argue the optimal doping for this state. We discuss our result in connection with static impurities, and show the likely relevance to the diluted kagome lattice Heisenberg model, describing actual compounds.

DOI
10.1103/physrevlett.111.097204

Related papers

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

Impurity-doped kagome antiferromagnet: A quantum dimer model approach

Didier Poilblanc, Arnaud Ralko

The doping of quantum Heisenberg antiferromagnets on the kagome lattice by nonmagnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing (a) the valence-bond crystal (VBC), (b) the dimer liquid, and (c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the kagome lattice to account for spontaneous creation of mobile $S=1/2$ spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos exact diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small-size spinon-impurity bound state appears in some region of the dimer-liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the valence-bond glass scenario [R. R. P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the nuclear magnetic resonance spectra of the Herbertsmithite compound are outlined.

arXiv:1006.5370•Physical Review B•Nov 19, 2010•27 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

Kagome lattice Hubbard model at half filling

Siegfried Guertler

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.

arXiv:1402.6612•Physical Review B•Aug 8, 2014•14 citations

Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid

Hong‐Chen Jiang, Thomas Devereaux, Steven Allan Kivelson

We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t-J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ=0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. Our results may be relevant to kagome lattice herbertsmithite upon doping.

arXiv:1702.06577•Physical Review Letters•Aug 7, 2017•49 citations

Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet

Tao Liu, Wei Li, Andreas Weichselbaum +2 more

We investigate the ground-state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site ${e}_{0}=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}90(2)$, with ${D}^{*}=8$ multiplets retained (i.e., a bond dimension of $D=24)$, and ${e}_{0}=\ensuremath{-}1.4116(4)$ from large-$D$ extrapolation, by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\ensuremath{\delta}\ensuremath{\approx}19%$, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state to be a simplex valence-bond crystal. We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground-state phase diagram. Moreover, we implement non-Abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.

arXiv:1406.5905•Physical Review B•Feb 23, 2015•56 citations
We investigate the ground state properties of the kagome lattice t - J model at low doping by variational Monte Carlo calculations. The resulting state possesses an interesting balance of spin exchange and kinetic exchange through the building blocks of stars which are linked by triangles and their internal hexagons. While the spin exchange is taking place mainly on the stars, hopping is favored on the hexagons. There is a density modulation, resulting in the holes having an effective static contribution. From this observation, how holes lead to dimerization in this model and why a particular valence bond crystal pattern is formed can be understood. Furthermore, we argue the optimal doping for this state. We discuss our result in connection with static impurities, and show the likely relevance to the diluted kagome lattice Heisenberg model, describing actual compounds.
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.
The doping of quantum Heisenberg antiferromagnets on the kagome lattice by nonmagnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing (a) the valence-bond crystal (VBC), (b) the dimer liquid, and (c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the kagome lattice to account for spontaneous creation of mobile S=1/2S=1/2S=1/2 spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos exact diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small-size spinon-impurity bound state appears in some region of the dimer-liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the valence-bond glass scenario [R. R. P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the nuclear magnetic resonance spectra of the Herbertsmithite compound are outlined.
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.
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 $t\text{\ensuremath{-}}J$ 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.
We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t-J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ=0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. Our results may be relevant to kagome lattice herbertsmithite upon doping.
We investigate the ground-state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site ${e}_{0}=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}90(2)$, with D∗=8{D}^{*}=8D∗=8 multiplets retained (i.e., a bond dimension of D=24)D=24)D=24), and ${e}_{0}=\ensuremath{-}1.4116(4)$ from large-DDD extrapolation, by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\ensuremath{\delta}\ensuremath{\approx}19%$, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state to be a simplex valence-bond crystal. We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground-state phase diagram. Moreover, we implement non-Abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.