One-dimensional lattice model with an exact matrix-product ground state describing the Laughlin wave function

Abstract

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 $\nu =1/q$) 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 $Z_2$ 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 reflects gapless edge states as was discussed by Li and Haldane.

11 pages, 4 figures

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Cited by in corpus (9)

• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Repulsive Interactions in Quantum Hall Systems as a Pairing Problem
• Geometric construction of Quantum Hall clustering Hamiltonians
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Devil's staircases in synthetic dimensions and gauge fields
• Solvable models for unitary and non-unitary topological phases
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Quantum Hall correlations in tilted extended Bose-Hubbard chains