Decomposition of the Fock Space in Two-Dimensional Square Lattice Systems |
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Authors: | B Kim M H Chung J H Kwon |
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Institution: | (1) Department of Physics, Hong-Ik University, Chochiwon, Choongnam, 339-701, South Korea;(2) Department of Mathematics, The University of Seoul, Dongdaemun-gu, Seoul, 130-743, South Korea |
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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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Keywords: | 20C30 20C35 81R05 |
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