### 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) |
---|---|

Pages (from-to) | 13660-13663 |

Number of pages | 4 |

Journal | Physical Review B |

Volume | 43 |

Issue number | 16 |

DOIs | |

State | Published - 1991 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

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

**Finite-size effects on the optical conductivity of a half-filled Hubbard ring.** / Stafford, Charles A; Millis, A. J.; Shastry, B. S.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 43, no. 16, pp. 13660-13663. https://doi.org/10.1103/PhysRevB.43.13660

}

TY - JOUR

T1 - Finite-size effects on the optical conductivity of a half-filled Hubbard ring

AU - Stafford, Charles A

AU - Millis, A. J.

AU - Shastry, B. S.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000238739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000238739&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.43.13660

DO - 10.1103/PhysRevB.43.13660

M3 - Article

AN - SCOPUS:0000238739

VL - 43

SP - 13660

EP - 13663

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 16

ER -