The spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>Heisenberg antiferromagnet on a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:mfrac></mml:math>-depleted triangular lattice: Ground-state properties

Schmalfuß, D.; Tomczak, P.; Schulenburg, J.; Richter, Johannes

doi:10.1103/physrevb.65.224405

Cited by 33 publications

(31 citation statements)

References 28 publications

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“…are non-negative, we conclude ||(s ∼ 4,5,6. Hence, for arbitrary Ψ ∈ H ij , the matrix D with entries…”

Section: Necessary Conditions For Tgs Systemsmentioning

confidence: 64%

Exact ground states for coupled spin trimers

Schmidt¹,

Richter²

2010

J. Phys. A: Math. Theor.

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Abstract. We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states.The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers s and their ground state Φ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to Φ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for Φ being a ground state. The classical case s → ∞ can be completely analyzed. For the quantum case we consider a couple of examples, where the critical values of the inter-trimer couplings are numerically determined. These examples include chains of corner sharing tetrahedra as well as certain spin tubes. Φ is proven to be gapped in the case of trimer chains. This follows from a more general theorem on quantum chains with product ground states.

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“…are non-negative, we conclude ||(s ∼ 4,5,6. Hence, for arbitrary Ψ ∈ H ij , the matrix D with entries…”

Section: Necessary Conditions For Tgs Systemsmentioning

confidence: 64%

Exact ground states for coupled spin trimers

Schmidt¹,

Richter²

2010

J. Phys. A: Math. Theor.

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“…As has been pointed out by D. Betts 35 a regular depletion of the triangular lattice by a factor of 1/7 yields another translationally invariant lattice, namely the Archimedian maple-leaf lattice. 4,36 The coordination number of this lattice is z = 5 and lies between those of the triangular (z = 6) and the kagomé (z = 4) lattices. Moreover, there is a frustrated Archimedian lattice with z = 4, the so-called bounce lattice.…”

Section: -22mentioning

confidence: 94%

“…However, there are indications from previous studies (based on exact diagonalizations of finite-sized lattices) of semi-classical GS magnetic LRO 4,36 in the spin-1 2 HAF on these lattices. This conclusion was drawn based on only two finite lattices of N = 18 and N = 36 sites and therefore the conviction in the conclusions is lessened.…”

mentioning

confidence: 96%

Spin-half Heisenberg antiferromagnet on two archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

et al. 2011

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We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized J-J ′ model interpolating between both systems by varying J ′ /J from J ′ /J = 0 (bounce limit) to J ′ /J = 1 (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the "pure" bounce (J ′ /J = 0) and maple-leaf (J ′ /J = 1) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range 0 ≤ J ′ /J J ′ c /J and that the magnetic order parameter varies only weakly with J ′ /J. At J ′ c ≈ 1.45J a direct first-order transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place. The orthogonal-dimer state is the exact ground state in this large-J ′ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We a find a 1/3 magnetization plateau for J ′ /J 1.07 and another one at 2/3 of saturation emerging only at large J ′ /J 3.

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“…These studies are motivated by the recent progress in synthesizing quasi-two-dimensional magnetic materials which exhibit exciting quantum effects [3][4][5][6][7][8][9][10]. Even spin systems on more exotic frustrated lattices such as the star lattice [11,12], the maple-leaf lattice [13,11] and the triangulated kagomé lattice [14] have been synthesized recently [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

The Heisenberg antiferromagnet on the square-kagomé lattice

Richter¹,

Schulenburg²,

Tomczak³

et al. 2009

Condens. Matter Phys.

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We discuss the ground state, the low-lying excitations as well as high-field thermodynamics of the Heisenberg antiferromagnet on the two-dimensional square-kagomé lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is also known for the Heisenberg antiferromagnet on the kagomé and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet with a finite spin gap and with a large number of non-magnetic excitations within this gap. We also discuss the magnetization versus field curve that shows a plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states. These localized states are highly degenerate and lead to interesting features in the low-temperature thermodynamics at high magnetic fields such as an additional low-temperature peak in the specific heat and an enhanced magnetocaloric effect.

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The spin-12Heisenberg antiferromagnet on a17-depleted triangular lattice: Ground-state properties

Cited by 33 publications

References 28 publications

Exact ground states for coupled spin trimers

Exact ground states for coupled spin trimers

Spin-half Heisenberg antiferromagnet on two archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

The Heisenberg antiferromagnet on the square-kagomé lattice

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