### Abstract

We use the Bethe-ansatz equations to calculate the total and zero-frequency spectral weight in the optical conductivity of the half-filled one-dimensional Hubbard model as a function of the lattice size L and the on-site repulsion U. The zero-frequency spectral weight D scales as L1/2exp(-L/) as L. Near U=0, varies as the inverse of the Lieb-Wu charge gap. In the strongly correlated regime (Ut), -1=ln(U/t)-1.48. $D is negative when L is a multiple of 4, corresponding to a negative inductance. We give a physical explanation of our results in terms of a simple model of ring exchange. The finite-size corrections to the total spectral weight scale as L-2. We discuss the implications of our results for exact diagonalization calculations of the optical conductivity.

Original language | English (US) |
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Pages (from-to) | 13660-13663 |

Number of pages | 4 |

Journal | Physical Review B |

Volume | 43 |

Issue number | 16 |

DOIs | |

State | Published - Jan 1 1991 |

Externally published | Yes |

### ASJC Scopus subject areas

- Condensed Matter Physics

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## Cite this

*Physical Review B*,

*43*(16), 13660-13663. https://doi.org/10.1103/PhysRevB.43.13660