| Using truncated conformal field theory, we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of . The auxiliary bond space is the Hilbert space of the descendants of primary fields and matrix elements can be calculated using well-known CFT commutation relations. We obtain a site-independent MPS representation on the thin annulus, cylinder and torus, while a site-dependent representation is possible on the disk and sphere geometries. We discuss the complications that arise due to the presence of null vectors in the theory's hilbert space, and present an array of procedures which optimize the numerical calculation of matrix elements. We investigate the spectrum of the MPS transfer matrix, its gap and its degeneracies. We show how to obtain, in the MPS representation, the Orbital, Particle, and Real Space entanglement spectrum in both the finite and infinite systems. By truncating the Hilbert space of the CFT, we then build an approximate MPS representation for Laughlin, Moore-Read, Read-Rezayi, Gaffnian and a series of superconformal minimal models and analyze their entanglement spectra, entanglement entropy, Renyi entropies and eigenvalue scaling, with a focus on the difference between unitary and non-unitary models. |
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