Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice

Honecker, A.; Cabra, D. C.; Everts, H. U.; Pujol, Pierre; Stauffer, Franck

doi:10.1103/physrevb.84.224410

Cited by 10 publications

(6 citation statements)

References 66 publications

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“…5,6 Since the kagome-lattice antiferromagnet is a typical two-dimensional frustrated system, most theoretical studies have been carried out mainly by the basis of the numerical-diagonalization method. [7][8][9][10][11][12][13][14][15][16][17][18][19][20] The brief behavior of the magnetization process of the kagome-lattice antiferromagnet was clarified in Ref. 9, which showed the existence of the magnetization plateau at one-third of the height of the saturation.…”

Section: Introductionmentioning

confidence: 99%

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Anomalous Behavior of the Magnetization Process of the S = 1/2 Kagome-Lattice Heisenberg Antiferromagnet at One-Third Height of the Saturation

Nakano

Sakai

2014

J. Phys. Soc. Jpn.

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The magnetization process of the S = 1/2 Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. We successfully obtain a new result of the magnetization process of a 42-site cluster in the entire range. Our analysis clarifies that the critical behavior around one-third of the height of the saturation is different from the typical behavior of the well-known magnetization plateau in two-dimensional systems. We also examine the effect of the √ 3 × √ 3-type distortion added to the kagome lattice. We find at one-third of the height of the saturation in the magnetization process that the undistorted kagome point is just the boundary between two phases that show their own properties that are different from each other. Our results suggest a relationship between the anomalous critical behavior at the undistorted point and the fact that the undistorted point is the boundary.

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Section: Introductionmentioning

confidence: 99%

“…The authors of Ref. 19, however, considered that the width of the plateau survives from the studies based on the model with easy-axis exchange anisotropies, 10,13 although the authors did not mention the behavior just outside of the plateau.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Behavior of the Magnetization Process of the S = 1/2 Kagome-Lattice Heisenberg Antiferromagnet at One-Third Height of the Saturation

Nakano

Sakai

2014

J. Phys. Soc. Jpn.

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“…which shows two extended plateaus (Fig. 11) corresponding to the magnetizations per trimer m ∆ = 1/2 and m ∆ = 3/2, respectively [11]. At the boundaries of these plateaus, the competition between different magnetization sectors renders the energetic contributions due to the small intertrimer coupling more important.…”

Section: B Thermodynamicsmentioning

confidence: 98%

“…This is, however, not true for all kinds of distortions, as seen for example in the "breathing-distorted" kagome lattice, where upward and downward triangles both remain equilateral but inequivalent to each other (Fig. 1(a)) [9][10][11]. Even under strong such breathing distortion, a quantum spin-liquid phase of the kagome lattice is expected to be stable [12,13].…”

Section: Introductionmentioning

confidence: 99%

Cluster quantum Monte Carlo study of two-dimensional weakly-coupled frustrated trimer antiferromagnets

Weber,

Caci,

Wessel

2022

Preprint

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We report results from spin trimer-based cluster quantum Monte Carlo simulations for the thermodynamic properties of two-dimensional frustrated quantum antiferromagnets that are composed of weakly-coupled three-spin (trimer) clusters. In particular, we consider the spin-1/2 kagome lattice with a strong breathing distortion, and the triangle-square lattice model proposed previously for the cuprate La4Cu3MoO12. For both cases, we demonstrate that an appropriately chosen trimer-based computational basis allows us to significantly reduce the quantum Monte Carlo sign problem down to the low-temperature regime. Besides exploring the thermodynamic behavior for the triangle-square lattice model we also assess a mean field theory-based prediction for the onset of chiral order. For the breathing distorted kagome lattice model, we observe a robust two-peak structure in the specific heat, both in the quantum spin liquid and the lattice-nematic regimes.

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“…Frustration is one of the simplest concepts in physics with far reaching consequences. 1,2 It is well known that antiferromagnetic (AF) exchange for three spins on a triangle is geometrically frustrated, both in classical Ising and in quantum Heisenberg models. On a two-dimensional (2D) square lattice, frustration typically involves interactions between further neighbors competing with those between nearest neighbors, but it can also occur with only the latter ones: for instance when, compared to the Ising model, the sign of spin exchange along every second column is reversed.…”

Section: Introductionmentioning

confidence: 99%

Magnetic properties of nanoscale compass-Heisenberg planar clusters

2012

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We study a model of spins 1/2 on a square lattice, generalizing the quantum compass model via the addition of perturbing Heisenberg interactions between nearest neighbors, and investigate its phase diagram and magnetic excitations. This model has motivations both from the field of strongly correlated systems with orbital degeneracy and from that of solid-state based devices proposed for quantum computing. We find that the high degeneracy of ground states of the compass model is fragile and changes into twofold degenerate ground states for any finite amplitude of Heisenberg coupling. By computing the spin structure factors of finite clusters with Lánczos diagonalization, we evidence a rich variety of phases characterized by Z2 symmetry, that are either ferromagnetic, C-type antiferromagnetic, or of Néel type, and analyze the effects of quantum fluctuations on phase boundaries. In the ordered phases the anisotropy of compass interactions leads to a finite excitation gap to spin waves. We show that for small nanoscale clusters with large anisotropy gap the lowest excitations are column-flip excitations that emerge due to Heisenberg perturbing interactions from the manifold of degenerate ground states of the compass model. We derive an effective one-dimensional XYZ model which faithfully reproduces the exact structure of these excited states and elucidates their microscopic origin. The low energy column-flip or compass-type excitations are robust against decoherence processes and are therefore well designed for storing information in quantum computing. We also point out that the dipolar interactions between nitrogen-vacancy centers forming a rectangular lattice in a diamond matrix may permit a solid-state realization of the anisotropic compass-Heisenberg model.

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Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice

Abstract: International audienc

Cited by 10 publications

References 66 publications

Anomalous Behavior of the Magnetization Process of the S = 1/2 Kagome-Lattice Heisenberg Antiferromagnet at One-Third Height of the Saturation

Anomalous Behavior of the Magnetization Process of the S = 1/2 Kagome-Lattice Heisenberg Antiferromagnet at One-Third Height of the Saturation

Cluster quantum Monte Carlo study of two-dimensional weakly-coupled frustrated trimer antiferromagnets

Magnetic properties of nanoscale compass-Heisenberg planar clusters

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