Supersymmetry "protected" topological phases of isostatic lattices and kagome antiferromagnets

Abstract

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 problem of balls and springs and its connection to local constraints satisfied by ground states. The Witten index of the SUSY model demands the Maxwell-Calladine index of mechanical structures. "Spontaneous supersymmetry breaking" is identified as the need to gap all modes in the bulk to create the topological isostatic lattice state. Since ground states of magnetic systems also satisfy local constraint conditions (such as the vanishing of the total spin on a triangle) I identify a similar SUSY structure for many common models of antiferromagnets including the square, triangluar, kagome, pyrochlore nearest neighbor antiferromagnets, and the $J_2=J_1/2$ square lattice antiferromagnet. Remarkably, the kagome family of antiferromagnets is the analog of topological isostatic lattices among this collections of models. Thus, a solid state realization of the theory of phonon topological band structure may be found in frustrated magnetic materials.

16 pages, 7 figures

References in corpus (8)

• Topological Photonics
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Topological Magnon Insulator in Insulating Ferromagnet
• Nonlinear conduction via solitons in a topological mechanical insulator
• Selective buckling via states of self-stress in topological metamaterials
• Topological mechanics of origami and kirigami
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Giant magnetic anisotropy of the bulk antiferromagnets IrMn and IrMn3

Cited by in corpus (10)

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• Jammed spin liquid in the bond-disordered kagome Heisenberg antiferromagnet
• A classification of magnetic frustration and metamaterials from topology
• Topology and geometry of spin origami
• Entanglement dualities in supersymmetry
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• From orthosymplectic structure to super topological matter