A quantum spin liquid (QSL) is an exotic quantum state of matter characterized by fluctuating spins which may exhibit long-range entanglement. Among the possible host candidates for a QSL ground state, the $S$ =1/2 kagome lattice antiferromagnet is particularly promising. Using high resolution inelastic neutron scattering measurements on Zn-barlowite (Zn $_\mathrm{x}$ Cu $_\mathrm{4-x}$ (OD) $_\mathrm{6}$ FBr, $x\simeq 0.80$ ), we measure a spin excitation spectrum consistent with a QSL ground state. Continuum scattering above $\sim $1 meV matches that of herbertsmithite (Zn$ _\mathrm{x} $Cu$ _\mathrm{4-x} $(OD)$ _6 $Cl$ _2$, $x\simeq 0.85$ ), another prominent kagome QSL material, indicating universal spinon excitations. A detailed analysis of the spin-spin correlations, compared with density matrix renormalization group calculations, further indicate a QSL ground state for the physically relevant Hamiltonian parameters. The measured spectra in Zn-barlowite are consistent with gapped behavior with a gap size $Δ= 1.1(2)$ meV. Comparison with a simple pair correlation model allows us to clearly distinguish intrinsic kagome correlations from impurity-induced correlations. Our results clarify the behavior that is universal within this important family of QSL candidate materials.A quantum spin liquid (QSL) is an exotic quantum state of matter characterized by fluctuating spins which may exhibit long-range entanglement. Among the possible host candidates for a QSL ground state, the $S$=1/2 kagome lattice antiferromagnet is particularly promising. Using high resolution inelastic neutron scattering measurements on Zn-barlowite (Zn$_\mathrm{x}$Cu$_\mathrm{4-x}$(OD)$_\mathrm{6}$FBr, $x\simeq 0.80$), we measure a spin excitation spectrum consistent with a QSL ground state. Continuum scattering above $\sim$1 meV matches that of herbertsmithite (Zn$_\mathrm{x}$Cu$_\mathrm{4-x}$(OD)$_6$Cl$_2$, $x\simeq 0.85$), another prominent kagome QSL material, indicating universal spinon excitations. A detailed analysis of the spin-spin correlations, compared with density matrix renormalization group calculations, further indicate a QSL ground state for the physically relevant Hamiltonian parameters. The measured spectra in Zn-barlowite are consistent with gapped behavior with a gap size $Δ= 1.1(2)$ meV. Comparison with a simple pair correlation model allows us to clearly distinguish intrinsic kagome correlations from impurity-induced correlations. Our results clarify the behavior that is universal within this important family of QSL candidate materials.

arXiv:2504.06491Apr 8, 20250 citations

Signatures of quantum spin liquids in small lattices

A. Yuste, David Castells-Graells, Anna Sanpera

Jun 18, 20181 citation

A unification of Z2 spin liquids on Kagome lattice

Gil Young Cho, Yuan-Ming Lu, Ashvin Vishwanath

Bulletin of the American Physical SocietyMar 6, 20140 citations

Static and dynamical spin correlations of the S = 1 2 random-bond antiferromagnetic Heisenberg model on the triangular and kagome lattices

Tokuro Shimokawa, Ken Watanabe, Hikaru Kawamura

Inspired by the recent theoretical suggestion that the random-bond $S=1/2$ antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this ``random-singlet state'' might be relevant to the QSL behaviors experimentally observed in triangular organic salts $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}{\mathrm{EtMe}}_{3}\mathrm{Sb}{[\mathrm{Pd}{(\mathrm{dmit})}_{2}]}_{2}$ and in kagome herbertsmithite ${\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{2}$ , we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, $S(\mathbf{q})$ and $S(\mathbf{q},\ensuremath{\omega})$, by means of an exact diagonalization method. In both triangular and kagome models, the computed $S(\mathbf{q},\ensuremath{\omega})$ in the random-singlet state depends on the wave vector $\mathbf{q}$ only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy $\ensuremath{\omega}$. Especially in the strongly random kagome model, $S(\mathbf{q},\ensuremath{\omega})$ hardly depends on $\mathbf{q}$ , and exhibits an almost flat distribution for a wide range of $\ensuremath{\omega}$, together with a $\ensuremath{\omega}=0$ peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.Inspired by the recent theoretical suggestion that the random-bond $S=1/2$ antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this ``random-singlet state'' might be relevant to the QSL behaviors experimentally observed in triangular organic salts $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}{\mathrm{EtMe}}_{3}\mathrm{Sb}{[\mathrm{Pd}{(\mathrm{dmit})}_{2}]}_{2}$ and in kagome herbertsmithite ${\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{2}$, we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, $S(\mathbf{q})$ and $S(\mathbf{q},\ensuremath{\omega})$, by means of an exact diagonalization method. In both triangular and kagome models, the computed $S(\mathbf{q},\ensuremath{\omega})$ in the random-singlet state depends on the wave vector $\mathbf{q}$ only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy $\ensuremath{\omega}$. Especially in the strongly random kagome model, $S(\mathbf{q},\ensuremath{\omega})$ hardly depends on $\mathbf{q}$, and exhibits an almost flat distribution for a wide range of $\ensuremath{\omega}$, together with a $\ensuremath{\omega}=0$ peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.

arXiv:1506.03576Physical Review BOct 9, 2015102 citations

Magnetic Correlations in the Hubbard Model on Triangular and Kagome Lattices

禎通前川

Physical Review LettersJan 1, 20050 citations

S

=1/2 kagome lattice antiferromagnet is particularly promising. Using high resolution inelastic neutron scattering measurements on Zn-barlowite (Zn

_\mathrm{x}

_\mathrm{4-x}

(OD)

_\mathrm{6}

FBr,

x\simeq 0.80

), we measure a spin excitation spectrum consistent with a QSL ground state. Continuum scattering above $\sim

1 meV matches that of herbertsmithite (Zn

_\mathrm{x}

Cu

_\mathrm{4-x}

(OD)

Cl

_2$,

x\simeq 0.85

), another prominent kagome QSL material, indicating universal spinon excitations. A detailed analysis of the spin-spin correlations, compared with density matrix renormalization group calculations, further indicate a QSL ground state for the physically relevant Hamiltonian parameters. The measured spectra in Zn-barlowite are consistent with gapped behavior with a gap size

Δ= 1.1(2)

meV. Comparison with a simple pair correlation model allows us to clearly distinguish intrinsic kagome correlations from impurity-induced correlations. Our results clarify the behavior that is universal within this important family of QSL candidate materials.

Inspired by the recent theoretical suggestion that the random-bond

S=1/2

antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this ``random-singlet state'' might be relevant to the QSL behaviors experimentally observed in triangular organic salts $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}{\mathrm{EtMe}}_{3}\mathrm{Sb}{[\mathrm{Pd}{(\mathrm{dmit})}_{2}]}_{2}$ and in kagome herbertsmithite

{\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{2}

, we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors,

S(\mathbf{q})

and $S(\mathbf{q},\ensuremath{\omega})$, by means of an exact diagonalization method. In both triangular and kagome models, the computed $S(\mathbf{q},\ensuremath{\omega})$ in the random-singlet state depends on the wave vector

\mathbf{q}

only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy $\ensuremath{\omega}$. Especially in the strongly random kagome model, $S(\mathbf{q},\ensuremath{\omega})$ hardly depends on

\mathbf{q}

, and exhibits an almost flat distribution for a wide range of $\ensuremath{\omega}$, together with a $\ensuremath{\omega}=0$ peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.