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:1410.7911 · Physical Review B

Phase diagram of the J 1 − J 2 Heisenberg model on the kagome lattice

Fabian Kolley, Stefan Depenbrock, Ian P. McCulloch, Ulrich Schollwöck, Vincenzo Alba

Published Mar 19, 2015• 79 citations
arXivHTMLPDF

Abstract

We perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-$1/2\phantom{\rule{0.16em}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at ${J}_{2}=0$. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around ${J}_{2}\ensuremath{\approx}0$, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic ${J}_{2}$, the ground state displays signatures of the magnetic order of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ and the $q=0$ type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the $q=0$ ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.

DOI
10.1103/physrevb.91.104418

Related papers

Density Matrix Renormalization Group Numerical Study of the Kagome Antiferromagnet

Hong‐Chen Jiang, Zheng-Yu Weng, D. N. Sheng

We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.

Physical Review Letters•Sep 10, 2008•271 citations

DMRG Numerical Study of the Kagomé Antiferromagnet

Hong‐Chen Jiang, Zheng-Yu Weng, D. N. Sheng

We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagomé lattice using the density-matrix renormalization group (DMRG) method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commersurate antiferromangetic wavevectors. We obtain a spin triplet excitation gap $ΔE(S=1)=0.055\pm 0.005$ by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.

arXiv:0804.1616•Apr 10, 2008•0 citations

Emergent quasi-one-dimensionality in a kagome magnet: A simple route to complexity

Shou-Shu Gong, Wei Kang Zhu, Kun Yang +3 more

We study the ground-state phase diagram of the quantum $\text{spin-}1/2$ Heisenberg model on the kagome lattice with first- $({J}_{1}<0)$, second- $({J}_{2}<0)$, and third-neighbor interactions $({J}_{d}>0)$ by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the ${J}_{d}\text{-dominant}$ regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions ${J}_{1,2}$. When either ${J}_{1}$ or ${J}_{2}$ is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime ${J}_{1}\ensuremath{\simeq}{J}_{2}$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories.

arXiv:1604.01459•Physical review. B./Physical review. B•Jul 27, 2016•27 citations

Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet

Simeng Yan, David A. Huse, Steven R. White

We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.

arXiv:1011.6114•Science•Apr 29, 2011•1,240 citations

Phase diagram of the spin- 12 J1 - J2 Heisenberg model on a honeycomb lattice

Shou-Shu Gong, D. N. Sheng, Olexei I. Motrunich +1 more

We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-$\frac{1}{2}$ Heisenberg model on a honeycomb lattice with first (${J}_{1}$) and second (${J}_{2}$) neighbor antiferromagnetic interactions, where a ${Z}_{2}$ spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size $N=2\ifmmode\times\else\texttimes\fi{}6\ifmmode\times\else\texttimes\fi{}6$. With increasing ${J}_{2}$, we find a N\'eel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ${m}_{s}^{2}$ on finite-size cylinders to the thermodynamic limit, we find the N\'eel order vanishing at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.22$. For $0.25<{J}_{2}/{J}_{1}\ensuremath{\le}0.35$, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For $0.22<{J}_{2}/{J}_{1}<0.25$, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.

arXiv:1306.6067•Physical Review B•Oct 29, 2013•113 citations

Gapless spin-liquid phase in the kagome spin- 12 Heisenberg antiferromagnet

Yasir Iqbal, Federico Becca, Sandro Sorella +1 more

We study the energy and the static spin structure factor of the ground state of the spin-$1/2$ quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) $U(1)$ Dirac spin liquid is competitive with previously proposed gapped (topological) ${\mathbb{Z}}_{2}$ spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site $E/J=\ensuremath{-}0.4365(2)$, which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.

arXiv:1209.1858•Physical Review B•Feb 14, 2013•331 citations
We perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-1/2J1\ensuremath-J21/2\phantom{\rule{0.16em}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}1/2J1​\ensuremath-J2​ Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J2=0{J}_{2}=0J2​=0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J2\ensuremath≈0{J}_{2}\ensuremath{\approx}0J2​\ensuremath≈0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J2{J}_{2}J2​, the ground state displays signatures of the magnetic order of the 3\ifmmode×\else\texttimes\fi3\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}3​\ifmmode×\else\texttimes\fi3​ and the q=0q=0q=0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q=0q=0q=0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagomé lattice using the density-matrix renormalization group (DMRG) method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commersurate antiferromangetic wavevectors. We obtain a spin triplet excitation gap ΔE(S=1)=0.055±0.005ΔE(S=1)=0.055\pm 0.005ΔE(S=1)=0.055±0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
We study the ground-state phase diagram of the quantum spin-1/2\text{spin-}1/2spin-1/2 Heisenberg model on the kagome lattice with first- (J1<0)({J}_{1}<0)(J1​<0), second- (J2<0)({J}_{2}<0)(J2​<0), and third-neighbor interactions (Jd>0)({J}_{d}>0)(Jd​>0) by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the Jd-dominant{J}_{d}\text{-dominant}Jd​-dominant regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions J1,2{J}_{1,2}J1,2​. When either J1{J}_{1}J1​ or J2{J}_{2}J2​ is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime ${J}_{1}\ensuremath{\simeq}{J}_{2}$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories.
We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.
We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-12\frac{1}{2}21​ Heisenberg model on a honeycomb lattice with first (J1{J}_{1}J1​) and second (J2{J}_{2}J2​) neighbor antiferromagnetic interactions, where a Z2{Z}_{2}Z2​ spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size $N=2\ifmmode\times\else\texttimes\fi{}6\ifmmode\times\else\texttimes\fi{}6$. With increasing J2{J}_{2}J2​, we find a N\'eel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ms2{m}_{s}^{2}ms2​ on finite-size cylinders to the thermodynamic limit, we find the N\'eel order vanishing at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.22$. For $0.25<{J}_{2}/{J}_{1}\ensuremath{\le}0.35$, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For 0.22<J2/J1<0.250.22<{J}_{2}/{J}_{1}<0.250.22<J2​/J1​<0.25, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.
We study the energy and the static spin structure factor of the ground state of the spin-1/21/21/2 quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) U(1)U(1)U(1) Dirac spin liquid is competitive with previously proposed gapped (topological) Z2{\mathbb{Z}}_{2}Z2​ spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site $E/J=\ensuremath{-}0.4365(2)$, which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.