Geometric Criterion for Solvability of Lattice Spin Systems
Masahiro Ogura,
Yukihisa Imamura,
Naruhiko Kameyama
et al.
Abstract:We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of adjacency matrices of the graphs provide conserved quantities of the systems. Furthermore, when the graphs belong to a class of simplicial complexes, the Hamiltonians are found to be mapped to bilinear forms of Majorana fermions, from which the full spectra of the systems are o… Show more
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