arXiv:1406.4767 · Physical Review B

Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice

Hitesh J. Changlani, Andreas Martin Läuchli

Published Mar 30, 2015• 53 citations

Abstract

We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The $\mathrm{SU}(3)$-symmetric point of this model Hamiltonian is a spontaneously trimerized state whose qualitative nature persists even at the Heisenberg point, a finding that contrasts previous proposals. We report the ground state energy per site of the Heisenberg model to be $\ensuremath{-}1.410(2)$ and establish the presence of a spin gap.

DOI: 10.1103/physrevb.91.100407

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arXiv:1406.4767 · Physical Review B

Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice

Hitesh J. Changlani, Andreas Martin Läuchli

Published Mar 30, 2015• 53 citations

arXiv HTML PDF

Abstract

We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The

\mathrm{SU}(3)

-symmetric point of this model Hamiltonian is a spontaneously trimerized state whose qualitative nature persists even at the Heisenberg point, a finding that contrasts previous proposals. We report the ground state energy per site of the Heisenberg model to be

\ensuremath{-}1.410(2)

and establish the presence of a spin gap.

DOI: 10.1103/physrevb.91.100407

Related papers

Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet

Tao Liu, Wei Li, Andreas Weichselbaum +2 more

We investigate the ground-state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site ${e}_{0}=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}90(2)$, with ${D}^{*}=8$ multiplets retained (i.e., a bond dimension of $D=24)$ , and ${e}_{0}=\ensuremath{-}1.4116(4)$ from large- $D$ extrapolation, by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\ensuremath{\delta}\ensuremath{\approx}19%$, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state to be a simplex valence-bond crystal. We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground-state phase diagram. Moreover, we implement non-Abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.We investigate the ground-state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site ${e}_{0}=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}90(2)$, with ${D}^{*}=8$ multiplets retained (i.e., a bond dimension of $D=24)$, and ${e}_{0}=\ensuremath{-}1.4116(4)$ from large-$D$ extrapolation, by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\ensuremath{\delta}\ensuremath{\approx}19%$, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state to be a simplex valence-bond crystal. We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground-state phase diagram. Moreover, we implement non-Abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.

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Yasir Iqbal, Federico Becca, Sandro Sorella +1 more

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arXiv:1209.1858Physical Review BFeb 14, 2013331 citations

We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The

\mathrm{SU}(3)

\ensuremath{-}1.410(2)

and establish the presence of a spin gap.

{D}^{*}=8

multiplets retained (i.e., a bond dimension of

D=24)

, and ${e}_{0}=\ensuremath{-}1.4116(4)$ from large-

D

extrapolation, by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\ensuremath{\delta}\ensuremath{\approx}19%$, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state to be a simplex valence-bond crystal. We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground-state phase diagram. Moreover, we implement non-Abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.

{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.

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.