Abstract
We discuss how to decompose the Fock space of a many-fermion system embedded in two-dimensional square lattice. Wefirst notice that the symmetry group inherent in the system is one of the two-dimensional space groups. We shortly review thecorresponding irreducible representations of the group. We then find the characters of the reducible representation of the many-fermion Fock space. Using the characters, we obtain the multiplicity of each irreducible representation contained in the Fock space of a fixed number of fermions. We present specific examples, where we calculate the multiplicities which are the dimensions of the decomposed spaces.
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Kim, B., Chung, M.H. & Kwon, J.H. Decomposition of the Fock Space in Two-Dimensional Square Lattice Systems. Lett Math Phys 78, 73–88 (2006). https://doi.org/10.1007/s11005-006-0104-4
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DOI: https://doi.org/10.1007/s11005-006-0104-4