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:cond-mat/0106293 · Journal of the Physical Society of Japan

Ground State Phase Transition in S=1 Distorted Kagomé Heisenberg Antiferromagnets

Kazuo Hida

Published Apr 1, 2002• 3 citations
arXivHTMLPDF

Abstract

The ground state phase transition in the distorted S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of the perturbational calculation and numerical exact diagonalization method. For strong $\sqrt{3} \times \sqrt{3}$ lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The presence of this transition supports the validity of the HSS picture of the ground state of the uniform S=1 KHAF.

DOI
10.1143/jpsj.71.1027

Related papers

Non-symmetry-breaking ground state of the S=1 Heisenberg model on the kagome lattice

Satoshi Nishimoto, Masaaki Nakamura

The $S=1$ antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account; periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is ${e}_{0}={E}_{0}/(NJ)=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}95$, which is readily lower than that of the TVBS state (${e}_{0}=\ensuremath{-}1.3912\ifmmode\pm\else\textpm\fi{}0.0025$). This agrees well with those of the cylindrical (${e}_{0}=\ensuremath{-}1.4122$) and periodic (${e}_{0}=\ensuremath{-}1.4111$) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the $S=1$ kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has $\mathrm{\ensuremath{\Delta}}/J=0.178\ifmmode\pm\else\textpm\fi{}0.005$, whereas the higher TVBS state has a larger one $\mathrm{\ensuremath{\Delta}}/J=0.280$.

arXiv:1409.5870•Physical Review B•Oct 21, 2015•23 citations

Possible chiral spin liquid state in the S = 1/2 kagome Heisenberg model

Rong-Yang Sun, Hui-Ke Jin, Hong-Hao Tu +1 more

Abstract The nature of the ground state for the S = 1/2 kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state might be a chiral spin liquid. Combining the density matrix renormalization group method and analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region. We characterize the nature of the ground state by computing energy derivatives, revealing ground-state degeneracy arising from spontaneous breaking of time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a √3 × √3 magnetically ordered phase and two valence-bond crystal phases.

•Sep 28, 2022•0 citations

Possible chiral spin liquid state in the S = 1/2 kagome Heisenberg model

Rong-Yang Sun, Hui-Ke Jin, Hong-Hao Tu +1 more

Abstract The nature of the ground state for the S = 1/2 Kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state is a chiral spin liquid. Combining the density matrix renormalization group method with analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region of the phase diagram. We characterize the nature of the ground state by computing energy derivatives, revealing the ground-state degeneracy arising from the spontaneous breaking of the time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a $$\sqrt{3}\times \sqrt{3}$$ 3 × 3 magnetically ordered phase and two valence-bond crystal phases.

arXiv:2203.07321•npj Quantum Materials•Feb 2, 2024•16 citations

Valence bond solid phases on deformed kagome lattices: Application to Rb2Cu3SnF12

Bohm‐Jung Yang, Yong Baek Kim

Motivated by a recent experiment on ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$, where spin-1/2 ${\text{Cu}}^{2+}$ moments reside on the layers of kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed kagome lattices. The deformation is characterized by a weaker exchange coupling $\ensuremath{\alpha}J$ on certain lattice links appropriate for ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ with $\ensuremath{\alpha}=1$ corresponding to the ideal kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operator mean-field theory. It is shown that the valence bond solid phase with a 36-site unit cell of the ideal kagome lattice is quite sensitive to a small lattice distortion as the kind discovered in ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$. As a result, we find that a more likely quantum ground state in ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ is the valence bond solid phase with a 12-site unit cell, where six dimers form a pinwheel structure, leading to strong modification of the elementary triplet and singlet excitation spectra in the deformed kagome lattices.

arXiv:0902.1752•Physical Review B•Jun 12, 2009•19 citations

Numerical linked-cluster expansion for the distorted kagome lattice Heisenberg model

Ehsan Khatami, Marcos Rigol

Motivated by experimental results for the thermodynamic properties of the Rb 2 Cu 3 SnF 12 material and the discovery of its valence-bond solid ground state, we utilize the numerical linked-cluster expansions (NLCEs) and devise an expansion tailored to solve the Heisenberg model on a pinwheel-distorted kagome lattice. Using the exchange interactions that are relevant to Rb 2 Cu 3 SnF 12 , we calculate its uniform spin susceptibility and find a very good agreement with experiment. Next, we focus on the ground state of a simplified model of the distorted kagome lattice and take advantage of a zero-temperature Lanczos-based NLCE to study the approach to the ground state of the uniform kagome lattice Heisenberg model using a tuning parameter. Together with results from exact diagonalization of finite clusters, we find evidence that a phase transition occurs before the uniform limit is reached.

Journal of Physics Conference Series•Dec 20, 2012•0 citations

Physics of low-energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet

Predrag Nikolić, T. Senthil

This paper is concerned with physics of the low-energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse-field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases---an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the original Kagome magnet which thereby exhibits a specific pattern of dimer ordering with a large unit cell. Comparisons with available numerical results are made.

arXiv:cond-mat/0305189•Physical review. B, Condensed matter•Dec 12, 2003•156 citations
The ground state phase transition in the distorted S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of the perturbational calculation and numerical exact diagonalization method. For strong 3×3\sqrt{3} \times \sqrt{3}3​×3​ lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The presence of this transition supports the validity of the HSS picture of the ground state of the uniform S=1 KHAF.
The S=1S=1S=1 antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account; periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is ${e}_{0}={E}_{0}/(NJ)=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}95$, which is readily lower than that of the TVBS state (${e}_{0}=\ensuremath{-}1.3912\ifmmode\pm\else\textpm\fi{}0.0025$). This agrees well with those of the cylindrical (${e}_{0}=\ensuremath{-}1.4122$) and periodic (${e}_{0}=\ensuremath{-}1.4111$) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the S=1S=1S=1 kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has $\mathrm{\ensuremath{\Delta}}/J=0.178\ifmmode\pm\else\textpm\fi{}0.005$, whereas the higher TVBS state has a larger one $\mathrm{\ensuremath{\Delta}}/J=0.280$.
Abstract The nature of the ground state for the S = 1/2 kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state might be a chiral spin liquid. Combining the density matrix renormalization group method and analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region. We characterize the nature of the ground state by computing energy derivatives, revealing ground-state degeneracy arising from spontaneous breaking of time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a √3 × √3 magnetically ordered phase and two valence-bond crystal phases.
Abstract The nature of the ground state for the S = 1/2 Kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state is a chiral spin liquid. Combining the density matrix renormalization group method with analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region of the phase diagram. We characterize the nature of the ground state by computing energy derivatives, revealing the ground-state degeneracy arising from the spontaneous breaking of the time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a 3×3\sqrt{3}\times \sqrt{3}3​×3​ 3 × 3 magnetically ordered phase and two valence-bond crystal phases.
Motivated by a recent experiment on Rb2Cu3SnF12{\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}Rb2​Cu3​SnF12​, where spin-1/2 Cu2+{\text{Cu}}^{2+}Cu2+ moments reside on the layers of kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed kagome lattices. The deformation is characterized by a weaker exchange coupling $\ensuremath{\alpha}J$ on certain lattice links appropriate for Rb2Cu3SnF12{\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}Rb2​Cu3​SnF12​ with $\ensuremath{\alpha}=1$ corresponding to the ideal kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operator mean-field theory. It is shown that the valence bond solid phase with a 36-site unit cell of the ideal kagome lattice is quite sensitive to a small lattice distortion as the kind discovered in Rb2Cu3SnF12{\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}Rb2​Cu3​SnF12​. As a result, we find that a more likely quantum ground state in Rb2Cu3SnF12{\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}Rb2​Cu3​SnF12​ is the valence bond solid phase with a 12-site unit cell, where six dimers form a pinwheel structure, leading to strong modification of the elementary triplet and singlet excitation spectra in the deformed kagome lattices.
Motivated by experimental results for the thermodynamic properties of the Rb 2 Cu 3 SnF 12 material and the discovery of its valence-bond solid ground state, we utilize the numerical linked-cluster expansions (NLCEs) and devise an expansion tailored to solve the Heisenberg model on a pinwheel-distorted kagome lattice. Using the exchange interactions that are relevant to Rb 2 Cu 3 SnF 12 , we calculate its uniform spin susceptibility and find a very good agreement with experiment. Next, we focus on the ground state of a simplified model of the distorted kagome lattice and take advantage of a zero-temperature Lanczos-based NLCE to study the approach to the ground state of the uniform kagome lattice Heisenberg model using a tuning parameter. Together with results from exact diagonalization of finite clusters, we find evidence that a phase transition occurs before the uniform limit is reached.
This paper is concerned with physics of the low-energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse-field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases---an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the original Kagome magnet which thereby exhibits a specific pattern of dimer ordering with a large unit cell. Comparisons with available numerical results are made.