تقرير
Supersymmetry on the lattice: Geometry, Topology, and Spin Liquids
| العنوان: | Supersymmetry on the lattice: Geometry, Topology, and Spin Liquids |
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| المؤلفون: | Roychowdhury, Krishanu, Attig, Jan, Trebst, Simon, Lawler, Michael J. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Condensed Matter - Strongly Correlated Electrons, Condensed Matter - Other Condensed Matter |
| الوصف: | In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons and fermions. Here we show how this fundamental concept can be applied to connect bosonic and fermionic lattice models in the realm of condensed matter physics, e.g., to identify a variety of (bosonic) phonon and magnon lattice models which admit topologically nontrivial free fermion models as superpartners. At the single-particle level, the bosonic and the fermionic models that are generated by the SUSY are isospectral except for zero modes, such as flat bands, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences and discuss further ramifications such as the definition of supersymmetric topological invariants for generic bosonic systems. Notably, a Hermitian form of the supercharge operator, the generator of the SUSY, can itself be interpreted as a hopping Hamiltonian on a bipartite lattice. This allows us to identify a wide class of interconnected lattices whose tight-binding Hamiltonians are superpartners of one another or can be derived via squaring or square-rooting their energy spectra all the while preserving band topology features. We introduce a five-fold way symmetry classification scheme of these SUSY lattice correspondences, including cases with a non-zero Witten index, based on a topological classification of the underlying Hermitian supercharge operator. These concepts are illustrated for various explicit examples including frustrated magnets, Kitaev spin liquids, and topological superconductors. Comment: 37 pages, 27 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.09475 |
| رقم الأكسشن: | edsarx.2207.09475 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |