arXiv:cond-mat/9511029

Spin Gap in CaV4O9: a Large S Appraoch

Marc Albrecht, Frédéric Mila

Published Nov 6, 1995• 0 citations

Abstract

We study the stability of the 4-site plaquette order in a model recently introduced by Katoh and Imada to explain the spin gap in CaV4O9. We show that all relevant types of order can be described within the framework of Schwinger boson mean fiel theory, and we make predictions regarding their relative stability. The results are compared to exact diagonalisation of finite cluster.

DOI: 10.48550/arxiv.cond-mat/9511029

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arXiv:cond-mat/9511029

Spin Gap in CaV4O9: a Large S Appraoch

Marc Albrecht, Frédéric Mila

Published Nov 6, 1995• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9511029

Related papers

Spin gap in Ca V4 O9 : A large- S approach

Marc Albrecht, Frédéric Mila

We study the stability of the four-site plaquette order in a model recently introduced by Katoh and Imada to explain the spin gap observed in ${\mathrm{Ca}{\mathrm{V}}_{4})}_{9}$ . We show that all relevant types of order (four-site plaquette, dimerized, N\'eel) can be described within the framework of Schwinger-boson mean-field theory, and we make predictions regarding their relative stability. The results are compared to exact diagonalization of finite clusters.We study the stability of the four-site plaquette order in a model recently introduced by Katoh and Imada to explain the spin gap observed in ${\mathrm{Ca}{\mathrm{V}}_{4})}_{9}$. We show that all relevant types of order (four-site plaquette, dimerized, N\'eel) can be described within the framework of Schwinger-boson mean-field theory, and we make predictions regarding their relative stability. The results are compared to exact diagonalization of finite clusters.

Physical review. B, Condensed matterFeb 1, 199636 citations

Spin Gap in Two-Dimensional Heisenberg Model for CaV4O9

Nobuyuki Katoh, Masatoshi Imada

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV $_4$ O $_9$ . From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.

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We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011)]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011)]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.

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I report results of a density matrix renormalization group (DMRG) study of a model for the two-dimensional spin-gapped system ${\mathrm{CaV}}_{4}{\mathrm{O}}_{9}$ . This study represents the first time that DMRG has been used to study a two-dimensional system on large lattices, in this case as large as $24\ifmmode\times\else\texttimes\fi{}11$, allowing extrapolation to the thermodynamic limit. I present a substantial improvement to the DMRG algorithms which makes these calculations feasible.I report results of a density matrix renormalization group (DMRG) study of a model for the two-dimensional spin-gapped system ${\mathrm{CaV}}_{4}{\mathrm{O}}_{9}$. This study represents the first time that DMRG has been used to study a two-dimensional system on large lattices, in this case as large as $24\ifmmode\times\else\texttimes\fi{}11$, allowing extrapolation to the thermodynamic limit. I present a substantial improvement to the DMRG algorithms which makes these calculations feasible.

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Indrani Bose, Asimkumar Ghosh

The experimental observation of a spin gap in the antiferromagnetic spin- $\frac{1}{2}$ compound CaV ${}_{4}$ O ${}_{9}$ has been attributed to the formation of a plaquette-resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin- $\frac{1}{2}$ model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.The experimental observation of a spin gap in the antiferromagnetic spin-$\frac{1}{2}$ compound CaV${}_{4}$O${}_{9}$ has been attributed to the formation of a plaquette-resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-$\frac{1}{2}$ model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.

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Ke Liu, Fa Wang

Motivated by recent experimental and numerical evidence of deconfined quantum critical points and quantum spin liquid states in the spin- $1/2$ Heisenberg model on the Shastry-Sutherland lattice, we studied possible symmetric spin liquid states and their proximate ordered states under Schwinger boson formalism. We found a symmetric gapped ${Z}_{2}$ spin liquid state for intermediate model parameter $0.66<{J}_{1}/{J}_{2}<0.71$ under the mean-field approximation. The Schwinger boson mean-field picture is partially supported by exact-diagonalization and self-consistent spin wave theory results.Motivated by recent experimental and numerical evidence of deconfined quantum critical points and quantum spin liquid states in the spin-$1/2$ Heisenberg model on the Shastry-Sutherland lattice, we studied possible symmetric spin liquid states and their proximate ordered states under Schwinger boson formalism. We found a symmetric gapped ${Z}_{2}$ spin liquid state for intermediate model parameter $0.66<{J}_{1}/{J}_{2}<0.71$ under the mean-field approximation. The Schwinger boson mean-field picture is partially supported by exact-diagonalization and self-consistent spin wave theory results.

arXiv:2308.16563Physical review. B./Physical review. BApr 5, 202412 citations

We study the stability of the four-site plaquette order in a model recently introduced by Katoh and Imada to explain the spin gap observed in

{\mathrm{Ca}{\mathrm{V}}_{4})}_{9}

. We show that all relevant types of order (four-site plaquette, dimerized, N\'eel) can be described within the framework of Schwinger-boson mean-field theory, and we make predictions regarding their relative stability. The results are compared to exact diagonalization of finite clusters.

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV

_4

_9

. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.

I report results of a density matrix renormalization group (DMRG) study of a model for the two-dimensional spin-gapped system

{\mathrm{CaV}}_{4}{\mathrm{O}}_{9}

. This study represents the first time that DMRG has been used to study a two-dimensional system on large lattices, in this case as large as $24\ifmmode\times\else\texttimes\fi{}11$, allowing extrapolation to the thermodynamic limit. I present a substantial improvement to the DMRG algorithms which makes these calculations feasible.

The experimental observation of a spin gap in the antiferromagnetic spin-

\frac{1}{2}

compound CaV

{}_{4}

{}_{9}

has been attributed to the formation of a plaquette-resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-

\frac{1}{2}

model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.

Motivated by recent experimental and numerical evidence of deconfined quantum critical points and quantum spin liquid states in the spin-

1/2

Heisenberg model on the Shastry-Sutherland lattice, we studied possible symmetric spin liquid states and their proximate ordered states under Schwinger boson formalism. We found a symmetric gapped

{Z}_{2}

spin liquid state for intermediate model parameter

0.66<{J}_{1}/{J}_{2}<0.71

under the mean-field approximation. The Schwinger boson mean-field picture is partially supported by exact-diagonalization and self-consistent spin wave theory results.