Physical review. B./Physical review. B

Quantum paramagnetic states in the spin- 12 distorted honeycomb-lattice Heisenberg antiferromagnet: Application to Cu2 (pymca) 3 ( ClO4)

Tokuro Shimokawa, Ken'ichi Takano, Zentaro Honda, Akira Okutani, Masayuki Hagiwara

Published Oct 12, 2022• 3 citations

Abstract

We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions, ${J}_{\mathrm{A}}, {J}_{\mathrm{B}}$, and ${J}_{\mathrm{C}}$, that is realized in a distorted honeycomb-lattice antiferromagnet ${\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4})$. We remeasured the magnetic susceptibility of its polycrystalline sample with special care and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the ${J}_{\mathrm{A}}/{J}_{\mathrm{C}}\text{\ensuremath{-}}{J}_{\mathrm{B}}/{J}_{\mathrm{C}}$ plane. The phase diagram consists of a small $\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}$ phase and a gapped quantum paramagnetic phase surrounding the $\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}$ phase. The latter includes six regimes of hexagonal-singlet-type states and dimer-singlet-type states alternatingly without boundaries closing the spin gap. We further calculate the equal-time spin structure factor in each phase using the QMC method. The computed spin dynamics by the exact diagonalization method exhibits continua near and in the AF phase. Characteristic four energy band structures in the state with strong hexagonal-singlet-type correlations are informative to clarify the ground state of ${\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4})$ by future neutron scattering measurements.

DOI: 10.1103/physrevb.106.134410

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Spin-gap phase of a quantum spin system on a honeycomb lattice

Ken'ichi Takano

arXiv:cond-mat/0609446Physical Review BOct 12, 200657 citations

Ground-state phases of the spin- 1 J 1 − J 2 Heisenberg antiferromagnet on the honeycomb lattice

P. H. Y. Li, R. F. Bishop

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Weakly coupled alternating S=12 chains in the distorted honeycomb lattice compound Na2Cu2TeO6

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Quantum phase transition, O(3) universality class, and phase diagram of the spin- 12 Heisenberg antiferromagnet on a distorted honeycomb lattice: A tensor renormalization-group study

Wei Li, Shou-Shu Gong, Yang Zhao +1 more

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Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: The J1 - J2 - J3 model

P. H. Y. Li, R. F. Bishop, DAMIAN J. J. FARNELL +1 more

arXiv:1204.2390Physical Review BOct 9, 201299 citations

Physical review. B./Physical review. B

Quantum paramagnetic states in the spin- 12 distorted honeycomb-lattice Heisenberg antiferromagnet: Application to Cu2 (pymca) 3 ( ClO4)

Tokuro Shimokawa, Ken'ichi Takano, Zentaro Honda, Akira Okutani, Masayuki Hagiwara

Published Oct 12, 2022• 3 citations

Publisher

Abstract

We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions,

{J}_{\mathrm{A}}, {J}_{\mathrm{B}}

, and

{J}_{\mathrm{C}}

, that is realized in a distorted honeycomb-lattice antiferromagnet

{\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4})

. We remeasured the magnetic susceptibility of its polycrystalline sample with special care and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the

{J}_{\mathrm{A}}/{J}_{\mathrm{C}}\text{\ensuremath{-}}{J}_{\mathrm{B}}/{J}_{\mathrm{C}}

plane. The phase diagram consists of a small

\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}

phase and a gapped quantum paramagnetic phase surrounding the

\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}

phase. The latter includes six regimes of hexagonal-singlet-type states and dimer-singlet-type states alternatingly without boundaries closing the spin gap. We further calculate the equal-time spin structure factor in each phase using the QMC method. The computed spin dynamics by the exact diagonalization method exhibits continua near and in the AF phase. Characteristic four energy band structures in the state with strong hexagonal-singlet-type correlations are informative to clarify the ground state of

{\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4})

by future neutron scattering measurements.

DOI: 10.1103/physrevb.106.134410

Related papers

Quantum paramagnetic states in the spin-1/2 distorted honeycomb-lattice Heisenberg antiferromagnet -- application to Cu $_2$ (pymca) $_3$ (ClO $_4$ )Quantum paramagnetic states in the spin-1/2 distorted honeycomb-lattice Heisenberg antiferromagnet -- application to Cu$_2$(pymca)$_3$(ClO$_4$)

Tokuro Shimokawa, Ken'ichi Takano, Zentaro Honda +2 more

We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions, $J_{\rm A}$ , $J_{\rm B}$ , and $J_{\rm C}$ that is realized in a distorted honeycomb-lattice antiferromagnet ${\rm Cu_2 (pymca)_3 (ClO_4)}$ . We remeasured the magnetic susceptibility of its polycrystalline sample with special care, and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the $J_{\rm A}/J_{\rm C}$ - $J_{\rm B}/J_{\rm C}$ plane. The phase diagram consists of a small N ${\rm \acute{e}}$ el phase and a gapped quantum paramagnetic phase surrounding the N ${\rm \acute{e}}$ el phase. The latter includes six regimes of hexagonal-singlet-type states and dimer-singlet-type states alternatingly without boundaries closing the spin gap. We further calculate the equal-time spin structure factor in each phase using the QMC method. The computed spin dynamics by the exact diagonalization method exhibits continuums near and in the AF phase. Characteristic four energy band structures in the state with strong hexagonal-singlet-type correlations are informative to clarify the ground-state of ${\rm Cu_2 (pymca)_3 (ClO_4)}$ by future neutron scattering measurements.We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions, $J_{\rm A}$, $J_{\rm B}$, and $J_{\rm C}$ that is realized in a distorted honeycomb-lattice antiferromagnet ${\rm Cu_2 (pymca)_3 (ClO_4)}$. We remeasured the magnetic susceptibility of its polycrystalline sample with special care, and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the $J_{\rm A}/J_{\rm C}$-$J_{\rm B}/J_{\rm C}$ plane. The phase diagram consists of a small N${\rm \acute{e}}$el phase and a gapped quantum paramagnetic phase surrounding the N${\rm \acute{e}}$el phase. The latter includes six regimes of hexagonal-singlet-type states and dimer-singlet-type states alternatingly without boundaries closing the spin gap. We further calculate the equal-time spin structure factor in each phase using the QMC method. The computed spin dynamics by the exact diagonalization method exhibits continuums near and in the AF phase. Characteristic four energy band structures in the state with strong hexagonal-singlet-type correlations are informative to clarify the ground-state of ${\rm Cu_2 (pymca)_3 (ClO_4)}$ by future neutron scattering measurements.

arXiv:2206.13064Jun 27, 20220 citations

Spin-gap phase of a quantum spin system on a honeycomb lattice

Ken'ichi Takano

We study a quantum spin system on a honeycomb lattice, when it includes frustration and distortion in antiferromagnetic (AF) exchange interactions. We transform the spin system onto a nonlinear $\ensuremath{\sigma}$ model (NLSM), preserving the original spin degrees of freedom. Assisted by a renormalization-group argument, the NLSM provides a ground-state phase diagram consisting of an ordered AF phase and a disordered spin-gap phase. The spin-gap phase extends from a strong frustration regime to a strong distortion regime, showing that the disordered ground states are essentially the same in both regimes. In the spin-1/2 case, the spin-gap phase for spin system on a honeycomb lattice is larger than that for the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model on a square lattice.We study a quantum spin system on a honeycomb lattice, when it includes frustration and distortion in antiferromagnetic (AF) exchange interactions. We transform the spin system onto a nonlinear $\ensuremath{\sigma}$ model (NLSM), preserving the original spin degrees of freedom. Assisted by a renormalization-group argument, the NLSM provides a ground-state phase diagram consisting of an ordered AF phase and a disordered spin-gap phase. The spin-gap phase extends from a strong frustration regime to a strong distortion regime, showing that the disordered ground states are essentially the same in both regimes. In the spin-1/2 case, the spin-gap phase for spin system on a honeycomb lattice is larger than that for the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model on a square lattice.

arXiv:cond-mat/0609446Physical Review BOct 12, 200657 citations

Ground-state phases of the spin- 1 J 1 − J 2 Heisenberg antiferromagnet on the honeycomb lattice

P. H. Y. Li, R. F. Bishop

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling ${J}_{1}>0$ and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling ${J}_{1}>0$ and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

arXiv:1602.08915Physical review. B./Physical review. BJun 28, 201621 citations

Weakly coupled alternating S=12 chains in the distorted honeycomb lattice compound Na2Cu2TeO6

Shang Gao, Ling-Fang Lin, Andrew F. May +5 more

Spin- $\frac{1}{2}$ chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement as the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb lattice compound ${\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}$ , but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here, we employ neutron scattering to study the spin dynamics in ${\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}$ and accurately determine the coupling strengths through the random phase approximation and density functional theory approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish ${\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}$ as a weakly coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.Spin-$\frac{1}{2}$ chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement as the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb lattice compound ${\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}$, but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here, we employ neutron scattering to study the spin dynamics in ${\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}$ and accurately determine the coupling strengths through the random phase approximation and density functional theory approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish ${\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}$ as a weakly coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.

arXiv:2010.06745Physical review. B./Physical review. BDec 2, 202019 citations

Quantum phase transition, O(3) universality class, and phase diagram of the spin- 12 Heisenberg antiferromagnet on a distorted honeycomb lattice: A tensor renormalization-group study

Wei Li, Shou-Shu Gong, Yang Zhao +1 more

The spin- $\frac{1}{2}$ Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the $O(3)$ universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.The spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the $O(3)$ universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.

arXiv:1005.0932Physical Review BMay 21, 201034 citations

Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: The J1 - J2 - J3 model

P. H. Y. Li, R. F. Bishop, DAMIAN J. J. FARNELL +1 more

We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 ${J}_{1}$ - ${J}_{2}$ - ${J}_{3}$ model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength ${J}_{1}\ensuremath{\equiv}1$, we find four magnetically ordered phases in the parameter window ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, namely, the N\'eel, striped, and N\'eel-II collinear AFM phases, plus a spiral phase. The N\'eel-II phase appears as a stable GS phase in the classical version of the model only for values ${J}_{3}<0$ . Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) $({J}_{2}^{{c}_{1}},{J}_{3}^{{c}_{1}})=(0.51\ifmmode\pm\else\textpm\fi{}0.01,0.69\ifmmode\pm\else\textpm\fi{}0.01)$ between the N\'eel, striped, and QP phases; (b) $({J}_{2}^{{c}_{2}},{J}_{3}^{{c}_{2}})=(0.65\ifmmode\pm\else\textpm\fi{}0.02,0.55\ifmmode\pm\else\textpm\fi{}0.01)$ between the striped, spiral, and QP phases; and (c) $({J}_{2}^{{c}_{3}},{J}_{3}^{{c}_{3}})=(0.69\ifmmode\pm\else\textpm\fi{}0.01,0.12\ifmmode\pm\else\textpm\fi{}0.01)$ between the spiral, N\'eel-II, and QP phases.We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 ${J}_{1}$-${J}_{2}$-${J}_{3}$ model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength ${J}_{1}\ensuremath{\equiv}1$, we find four magnetically ordered phases in the parameter window ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, namely, the N\'eel, striped, and N\'eel-II collinear AFM phases, plus a spiral phase. The N\'eel-II phase appears as a stable GS phase in the classical version of the model only for values ${J}_{3}<0$. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) $({J}_{2}^{{c}_{1}},{J}_{3}^{{c}_{1}})=(0.51\ifmmode\pm\else\textpm\fi{}0.01,0.69\ifmmode\pm\else\textpm\fi{}0.01)$ between the N\'eel, striped, and QP phases; (b) $({J}_{2}^{{c}_{2}},{J}_{3}^{{c}_{2}})=(0.65\ifmmode\pm\else\textpm\fi{}0.02,0.55\ifmmode\pm\else\textpm\fi{}0.01)$ between the striped, spiral, and QP phases; and (c) $({J}_{2}^{{c}_{3}},{J}_{3}^{{c}_{3}})=(0.69\ifmmode\pm\else\textpm\fi{}0.01,0.12\ifmmode\pm\else\textpm\fi{}0.01)$ between the spiral, N\'eel-II, and QP phases.

arXiv:1204.2390Physical Review BOct 9, 201299 citations

We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions,

{J}_{\mathrm{A}}, {J}_{\mathrm{B}}

, and

{J}_{\mathrm{C}}

, that is realized in a distorted honeycomb-lattice antiferromagnet

{\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4})

{J}_{\mathrm{A}}/{J}_{\mathrm{C}}\text{\ensuremath{-}}{J}_{\mathrm{B}}/{J}_{\mathrm{C}}

plane. The phase diagram consists of a small

\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}

phase and a gapped quantum paramagnetic phase surrounding the

\mathrm{N}\stackrel{\ifmmode \acute{}\else \'{}\fi{}}{\mathrm{e}}\mathrm{el}

{\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4})

by future neutron scattering measurements.

Quantum paramagnetic states in the spin-1/2 distorted honeycomb-lattice Heisenberg antiferromagnet -- application to Cu

_2

(pymca)

_3

(ClO

_4

)

We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions,

J_{\rm A}

J_{\rm B}

, and

J_{\rm C}

that is realized in a distorted honeycomb-lattice antiferromagnet

{\rm Cu_2 (pymca)_3 (ClO_4)}

. We remeasured the magnetic susceptibility of its polycrystalline sample with special care, and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the

J_{\rm A}/J_{\rm C}

J_{\rm B}/J_{\rm C}

plane. The phase diagram consists of a small N

{\rm \acute{e}}

el phase and a gapped quantum paramagnetic phase surrounding the N

{\rm \acute{e}}

el phase. The latter includes six regimes of hexagonal-singlet-type states and dimer-singlet-type states alternatingly without boundaries closing the spin gap. We further calculate the equal-time spin structure factor in each phase using the QMC method. The computed spin dynamics by the exact diagonalization method exhibits continuums near and in the AF phase. Characteristic four energy band structures in the state with strong hexagonal-singlet-type correlations are informative to clarify the ground-state of

{\rm Cu_2 (pymca)_3 (ClO_4)}

by future neutron scattering measurements.

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling

{J}_{1}>0

and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

Spin-

\frac{1}{2}

chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement as the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb lattice compound

{\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}

, but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here, we employ neutron scattering to study the spin dynamics in

{\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}

and accurately determine the coupling strengths through the random phase approximation and density functional theory approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish

{\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}

as a weakly coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.

The spin-

\frac{1}{2}

Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the

O(3)

universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.

We use the coupled-cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2

{J}_{1}

{J}_{2}

{J}_{3}

model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local onsite magnetization. With the nearest-neighbor coupling strength ${J}_{1}\ensuremath{\equiv}1$, we find four magnetically ordered phases in the parameter window ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, namely, the N\'eel, striped, and N\'eel-II collinear AFM phases, plus a spiral phase. The N\'eel-II phase appears as a stable GS phase in the classical version of the model only for values

{J}_{3}<0

. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at (a) $({J}_{2}^{{c}_{1}},{J}_{3}^{{c}_{1}})=(0.51\ifmmode\pm\else\textpm\fi{}0.01,0.69\ifmmode\pm\else\textpm\fi{}0.01)$ between the N\'eel, striped, and QP phases; (b) $({J}_{2}^{{c}_{2}},{J}_{3}^{{c}_{2}})=(0.65\ifmmode\pm\else\textpm\fi{}0.02,0.55\ifmmode\pm\else\textpm\fi{}0.01)$ between the striped, spiral, and QP phases; and (c) $({J}_{2}^{{c}_{3}},{J}_{3}^{{c}_{3}})=(0.69\ifmmode\pm\else\textpm\fi{}0.01,0.12\ifmmode\pm\else\textpm\fi{}0.01)$ between the spiral, N\'eel-II, and QP phases.