# Topology and Geometry of Spin Origami.

@article{Roychowdhury2018TopologyAG,
title={Topology and Geometry of Spin Origami.},
author={Krishanu Roychowdhury and D. Zeb Rocklin and Michael J. Lawler},
journal={Physical review letters},
year={2018},
volume={121 17},
pages={
177201
}
}
• Published 28 April 2017
• Medicine, Physics
• Physical review letters
Kagome antiferromagnets are known to be highly frustrated and degenerate when they possess simple, isotropic interactions. We consider the entire class of these magnets when their interactions are spatially anisotropic. We do so by identifying a certain class of systems whose degenerate ground states can be mapped onto the folding motions of a generalized "spin origami" two-dimensional mechanical sheet. Some such anisotropic spin systems, including Cs_{2}ZrCu_{3}F_{12}, map onto flat origami…
11 Citations

## Figures and Topics from this paper

Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
Majorana edge modes are candidate elements of topological quantum computing. In this paper, we propose a Floquet engineering approach to generate multiple non-Hermitian Majorana zero and
Dynamics and energy landscape of the jammed spin liquid
• Physics
Physical Review B
• 2019
We study the low temperature static and dynamical properties of the classical bond-disordered antiferromagnetic Heisenberg model on the kagome lattice. This model has recently been shown to host a
Topological mechanical metamaterials: A brief review
• Materials Science
• 2020
Abstract Topological mechanical metamaterials have emerged with the development of topological phases and topological phase transitions in modern condensed matter physics. Their attractive
Topology in Nonlinear Mechanical Systems.
• Physics, Medicine
Physical review letters
• 2021
This Letter presents a generic prescription to define topological indices that accommodates nonlinear effects in mechanical systems without taking any approximation, and predicts one type of topologically protected solitons that are robust to disorders.
Symmetry and Topology in Non-Hermitian Physics
• Physics, Mathematics
Physical Review X
• 2019
We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators
Amplitude-dependent boundary modes in topological mechanical lattices
• Physics
• 2021
Abstract Boundary modes localized at the edge or on the interface of topological mechanical lattices are analogous to their electronic counterparts in topological insulators and are robust and immune
Disordered flat bands on the kagome lattice
• Physics
Physical Review B
• 2018
In flat bands, the kinetic energy is fully quenched rendering interactions nonperturbative and resulting in complex many-body phenomena, such as the (fractional) quantum Hall effect. Here, the
Theory and practice of origami in science.
No longer just the purview of artists and enthusiasts, origami engineering has emerged as a potentially powerful tool to create three dimensional structures on disparate scales. Whether origami (and

## References

SHOWING 1-10 OF 92 REFERENCES
Topological Mechanics of Origami and Kirigami.
A recent connection between spring networks and quantum topological states is exploited to design origami with localized folding motions at boundaries and it is demonstrated how to generalize these topological design principles to two dimensions.
LOW-TEMPERATURE PROPERTIES OF CLASSICAL GEOMETRICALLY FRUSTRATED ANTIFERROMAGNETS
• Physics
• 1998
We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbor antiferromagnetic interactions on a class of geometrically frustrated lattices, which
Geometric mechanics of periodic pleated origami.
• Physics, Medicine
Physical review letters
• 2013
This work characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths.
Spin folding in the two-dimensional Heisenberg kagomé antiferromagnet.
• Physics, Medicine
Physical review. B, Condensed matter
• 1993
Spin-folding modes in the two-dimensional Heisenberg kagom\'e antiferromagnet favor coplanar spin configurations with three-spin tensor order and non-Abelian homotopy that exhibits a broad distribution of order parameters.
Classification of magnetic frustration and metamaterials from topology
• Physics
Physical Review B
• 2018
We study the relationship between the physics of topology and zero modes in frustrated systems and metama- terials. Zero modes that exist in topological matters are distinct from the ones arising
Partial ferromagnetic ordering and indirect exchange interaction in the spatially anisotropic kagome antiferromagnet Cs 2 Cu 3 CeF 12
We report the crystal structure and unconventional magnetic ordering of ${\text{Cs}}_{2}{\text{Cu}}_{3}{\text{CeF}}_{12}$, which is composed of buckled kagome lattice of ${\text{Cu}}^{2+}$ ions. The
Nonlinear conduction via solitons in a topological mechanical insulator
• Medicine, Physics
Proceedings of the National Academy of Sciences
• 2014
This work builds a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another and paves the way toward adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures.
Supersymmetry protected topological phases of isostatic lattices and kagome antiferromagnets
I generalize the theory of phonon topological band structures of isostatic lattices to frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon
Surface phonons, elastic response, and conformal invariance in twisted kagome lattices
• Kai Sun
• Medicine, Materials Science
Proceedings of the National Academy of Sciences
• 2012
Elasticity and phonons of a special class of two-dimensional isostatic lattices constructed by distorting the kagome lattice are explored and it is shown that the phonon structure of these lattices, characterized by vanishing bulk moduli and thus negative Poisson ratios, depends sensitively on boundary conditions and on the nature of the k Kagome distortions.
Transformable topological mechanical metamaterials
• Physics, Medicine
Nature communications
• 2017
It is shown that the existence and form of a soft deformation directly determines floppy edge modes and phonon dispersion, and the soft strain is generalized to generate domain structures that allow further tuning of the material.