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arXiv:cond-mat/9606012 · Physics Letters A

Exact ground states of one-dimensional quantum systems: matrix product approach

Gang Su

Published Apr 1, 1996• 10 citations
arXivHTMLPDF
DOI
10.1016/0375-9601(96)00085-0

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We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors $\ensuremath{\nu}=1/q$) on torus geometry. Surprisingly, the exactly solvable Hamiltonian has the same mathematical structure as that of the pseudopotential for the Laughlin wave function, and naturally derives the general properties of the Laughlin wave function such as the Z2{Z}_{2}Z2​ properties of the FQH states and the fermion-boson relation. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using the matrix product method, density functions and correlation functions are calculated analytically. Especially, obtained entanglement spectra reflect gapless edge states as was discussed by Li and Haldane.