Universal lowest energy configurations in a classical Heisenberg model describing frustrated systems with wheel geometry

Florek, Wojciech; Kamieniarz, G.; Marlewski, Adam

doi:10.1103/physrevb.100.054434

Cited by 9 publications

(12 citation statements)

References 64 publications

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“…This approach has been extensively discussed in Schmidt's works [26] and its application to heterogeneous systems have been recently presented [19], so only some important points are mentioned below. In a present version this approach can be applied to isotropic bilinear interactions when a general form of the energy function is given as:…”

Section: The Lagrange Variety Approachmentioning

confidence: 99%

“…At first glance it seems that this approach is even more difficult than standard analytical methods. However, the gauge vector coefficients have to obey the symmetry of the original problem, so a number of independent parameters is significantly reduced [19,25,26]. The lowest energy and the corresponding LEC (or LECs) of a given system are determined in three steps:…”

Section: The Lagrange Variety Approachmentioning

confidence: 99%

“…This specific eigenvaluej of J(λ) is used to calculate E LEC = (N + 1)j/2 [19,25]. Some important notes have to be made • This solution is unique, i.e., there is only one global maximum of j min , but the corresponding eigenvalue may be degenerate.…”

Section: The Lagrange Variety Approachmentioning

confidence: 99%

“…1) [13][14][15][16][17][18]. In general, heterometallic systems may be considered [19], but this short paper is limited to homogeneous ones. To avoid frustration in a peripheral ring only centered polygons XY 2q (corresponding to wheel graphs W 2q+1 [20]) are investigated.…”

Section: Introductionmentioning

confidence: 99%

“…This technique enables precise determination of the global minimum and the corresponding LEC considering a general form of the energy function for any system size [27]. Such approach has been successfully applied to heterometallic wheels [19] and some of the results obtained are shortly presented below.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Lagrange variety approach applied to frustrated classical wheels

Florek¹,

Marlewski²,

Kamieniarz³

et al. 2020

Nanosystems: Phys. Chem. Math.

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The Lagrange variety approach introduced by Schmidt and Luban [J. Phys. A: Math. Gen. 36, 6351 (2003)] is applied to geometrically frustrated wheels (centered regular polygons). It is shown that the lowest energy configurations are planar or collinear. The latter one, characteristic for nonfrustrated classical systems, is also observed in the presence of competing interactions in a well-determined range (0, αc) of the energy function parameter α. The 'critical' value αc = 1/4 is universal, i.e., it does not depend on a system size. In this domain, the geometric frustration is present, but there is no non-trivial degeneracy.

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Section: The Lagrange Variety Approachmentioning

confidence: 99%

Section: The Lagrange Variety Approachmentioning

confidence: 99%

Section: The Lagrange Variety Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Lagrange variety approach applied to frustrated classical wheels

Florek¹,

Marlewski²,

Kamieniarz³

et al. 2020

Nanosystems: Phys. Chem. Math.

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Embedded quantum-error correction and controlled-phase gate for molecular spin qubits

et al. 2021

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A scalable architecture for quantum computing requires logical units supporting quantum-error correction. In this respect, magnetic molecules are particularly promising, since they allow one to define logical qubits with embedded quantum-error correction by exploiting multiple energy levels of a single molecule. The single-object nature of this encoding is expected to facilitate the implementation of error correction procedures and logical operations. In this work, we make progress in this direction by showing how two-qubit gates between error-protected units can be realised, by means of easily implementable sequences of electro-magnetic pulses.

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Discontinuous quantum and classical magnetic response of the pentakis dodecahedron*

Konstantinidis¹

2021

J. Phys.: Condens. Matter

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The pentakis dodecahedron, the dual of the truncated icosahedron, consists of 60 edge-sharing triangles. It has 20 six-fold and 12 five-fold coordinated vertices, with the former forming a dodecahedron, and each of the latter connected to the vertices of one of the 12 pentagons of the dodecahedron. When spins mounted on the vertices of the pentakis dodecahedron interact according to the nearest-neighbor antiferromagnetic Heisenberg model, the two different vertex types necessitate the introduction of two exchange constants. As the relative strength of the two constants is varied the molecule interpolates between the dodecahedron and a molecule consisting only of quadrangles. The competition between the two exchange constants, frustration, and an external magnetic field results in a multitude of ground-state magnetization and susceptibility discontinuities. At the classical level the maximum is ten magnetization and one susceptibility discontinuities when the 12 five-fold vertices interact with the dodecahedron spins with approximately one-half the strength of their interaction. When the two interactions are approximately equal in strength the number of discontinuities is also maximized, with three of the magnetization and eight of the susceptibility. At the full quantum limit, where the magnitude of the spins equals 1 2 , there can be up to three ground-state magnetization jumps that have the z-component of the total spin changing by ΔS z = 2, even though quantum fluctuations rarely allow discontinuities of the magnetization. The full quantum case also supports a ΔS z = 3 discontinuity. Frustration also results in nonmagnetic states inside the singlet-triplet gap. These results make the pentakis dodecahedron the molecule with the largest number of magnetization and susceptibility discontinuities from the quantum to the classical level, taking its size also into account.

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Universal lowest energy configurations in a classical Heisenberg model describing frustrated systems with wheel geometry

Cited by 9 publications

References 64 publications

The Lagrange variety approach applied to frustrated classical wheels

The Lagrange variety approach applied to frustrated classical wheels

Embedded quantum-error correction and controlled-phase gate for molecular spin qubits

Discontinuous quantum and classical magnetic response of the pentakis dodecahedron*

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