Zheng-Yuan Wang, Masaaki Nakamura
We introduce a one-dimensional model with an exact ground state describing the fractional quantum Hall (FQH) states in Laughlin series (filling factors $\nu=1/q$) on torus geometry. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using matrix product method, density functions and correlation functions are calculated analytically. The exactly solvable Hamiltonian has same degrees of freedoms for parameters as those of the Trugman-Kivelson type pseudo potential, and it naturally derives general properties of Laughlin states such as the $Z_2$ classification and the fermion-boson relation.
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http://arxiv.org/abs/1206.3071
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