Journal of Physics Conference Series

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

Ehsan Khatami, Marcos Rigol

Published Dec 20, 2012• 0 citations

Abstract

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.

DOI: 10.1088/1742-6596/402/1/012018

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Journal of Physics Conference Series

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

Ehsan Khatami, Marcos Rigol

Published Dec 20, 2012• 0 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/402/1/012018

Related papers

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

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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.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.

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Nikita Astrakhantsev, Francesco Ferrari, Nils Niggemann +9 more

Quantum spin models on two-dimensional corner-sharing triangular arrangements, e.g., the kagome lattice, are fertile playgrounds for realizing exotic phases. Following the recent report of a gapless spin liquid in KCu ${}_{6}$ AlBiO ${}_{4}$ (SO ${}_{4}$ ) ${}_{5}$ Cl, wherein the Cu ${}^{2+}$ spin-\textonehalf{} ions form a perfect two-dimensional shuriken lattice, the authors employ state-of-the-art quantum many-body approaches to reveal a pinwheel valence-bond-crystal ground state of the isotropic Heisenberg antiferromagnet. This work thus points to the important role of spatial anisotropy in triggering the gapless spin liquid, in contrast to the kagome material herbertsmithite.Quantum spin models on two-dimensional corner-sharing triangular arrangements, e.g., the kagome lattice, are fertile playgrounds for realizing exotic phases. Following the recent report of a gapless spin liquid in KCu${}_{6}$AlBiO${}_{4}$(SO${}_{4}$)${}_{5}$Cl, wherein the Cu${}^{2+}$ spin-\textonehalf{} ions form a perfect two-dimensional shuriken lattice, the authors employ state-of-the-art quantum many-body approaches to reveal a pinwheel valence-bond-crystal ground state of the isotropic Heisenberg antiferromagnet. This work thus points to the important role of spatial anisotropy in triggering the gapless spin liquid, in contrast to the kagome material herbertsmithite.

arXiv:2110.08198Physical review. B./Physical review. BDec 22, 202137 citations

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.

{\mathrm{Sr}}_{2}\mathrm{Cu}({\mathrm{Te}}_{0.5}{\mathrm{W}}_{0.5}){\mathrm{O}}_{6}

. Our method can be used to study finite-temperature properties of other disordered quantum lattice models, including those for interacting lattice fermions.

\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.

{}_{6}

AlBiO

{}_{4}

(SO

{}_{4}

)

{}_{5}

Cl, wherein the Cu

{}^{2+}

spin-\textonehalf{} ions form a perfect two-dimensional shuriken lattice, the authors employ state-of-the-art quantum many-body approaches to reveal a pinwheel valence-bond-crystal ground state of the isotropic Heisenberg antiferromagnet. This work thus points to the important role of spatial anisotropy in triggering the gapless spin liquid, in contrast to the kagome material herbertsmithite.