# A recipe for constructing frustration-free Hamiltonians with gauge and matter fields in one and two dimensions

@article{Ferreira2015ARF, title={A recipe for constructing frustration-free Hamiltonians with gauge and matter fields in one and two dimensions}, author={Miguel Jorge Bernab'e Ferreira and Juan Pablo Ibieta Jimenez and Pramod Padmanabhan and Paulo Te{\^o}tonio Sobrinho}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2015}, volume={48} }

State sum constructions, such as Kuperberg’s algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights with different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space–time dimensions. The matter fields introduce new weights to the vertices and they correspond to Potts spin configurations described…

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