### Abstract

In this paper we show that the general finite-energy spectral-function expressions provided by the pseudofermion dynamical theory for the one-dimensional Hubbard model lead to the expected low-energy Tomonaga-Luttinger liquid correlation function expressions. Moreover, we use the former general expressions to derive correlation-function asymptotic expansions in space and time which go beyond those obtained by conformal-field theory and bosonization: we derive explicit expressions for the pre-factors of all terms of such expansions and find that they have an universal form, as the corresponding critical exponents. Our results refer to all finite values of the on-site repulsion U and to a chain of length L very large and with periodic boundary conditions for the above model, but are of general nature for many integrable interacting models. The studies of this paper clarify the relation of the low-energy Tomonaga-Luttinger liquid behavior to the scattering mechanisms which control the spectral properties at all energy scales and provide a broader understanding of the unusual properties of quasi-one-dimensional nanostructures, organic conductors, and optical lattices of ultracold fermionic atoms. Furthermore, our results reveal the microscopic mechanisms which are behind the similarities and differences of the low-energy and finite-energy spectral properties of the model metallic phase.

Original language | English |
---|---|

Pages (from-to) | 237-260 |

Number of pages | 24 |

Journal | Nuclear Physics B |

Volume | 737 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 13 2006 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*737*(3), 237-260. https://doi.org/10.1016/j.nuclphysb.2005.12.016

**The low-energy limiting behavior of the pseudofermion dynamical theory.** / Carmelo, J. M P; Martelo, L. M.; Penc, K.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 737, no. 3, pp. 237-260. https://doi.org/10.1016/j.nuclphysb.2005.12.016

}

TY - JOUR

T1 - The low-energy limiting behavior of the pseudofermion dynamical theory

AU - Carmelo, J. M P

AU - Martelo, L. M.

AU - Penc, K.

PY - 2006/3/13

Y1 - 2006/3/13

N2 - In this paper we show that the general finite-energy spectral-function expressions provided by the pseudofermion dynamical theory for the one-dimensional Hubbard model lead to the expected low-energy Tomonaga-Luttinger liquid correlation function expressions. Moreover, we use the former general expressions to derive correlation-function asymptotic expansions in space and time which go beyond those obtained by conformal-field theory and bosonization: we derive explicit expressions for the pre-factors of all terms of such expansions and find that they have an universal form, as the corresponding critical exponents. Our results refer to all finite values of the on-site repulsion U and to a chain of length L very large and with periodic boundary conditions for the above model, but are of general nature for many integrable interacting models. The studies of this paper clarify the relation of the low-energy Tomonaga-Luttinger liquid behavior to the scattering mechanisms which control the spectral properties at all energy scales and provide a broader understanding of the unusual properties of quasi-one-dimensional nanostructures, organic conductors, and optical lattices of ultracold fermionic atoms. Furthermore, our results reveal the microscopic mechanisms which are behind the similarities and differences of the low-energy and finite-energy spectral properties of the model metallic phase.

AB - In this paper we show that the general finite-energy spectral-function expressions provided by the pseudofermion dynamical theory for the one-dimensional Hubbard model lead to the expected low-energy Tomonaga-Luttinger liquid correlation function expressions. Moreover, we use the former general expressions to derive correlation-function asymptotic expansions in space and time which go beyond those obtained by conformal-field theory and bosonization: we derive explicit expressions for the pre-factors of all terms of such expansions and find that they have an universal form, as the corresponding critical exponents. Our results refer to all finite values of the on-site repulsion U and to a chain of length L very large and with periodic boundary conditions for the above model, but are of general nature for many integrable interacting models. The studies of this paper clarify the relation of the low-energy Tomonaga-Luttinger liquid behavior to the scattering mechanisms which control the spectral properties at all energy scales and provide a broader understanding of the unusual properties of quasi-one-dimensional nanostructures, organic conductors, and optical lattices of ultracold fermionic atoms. Furthermore, our results reveal the microscopic mechanisms which are behind the similarities and differences of the low-energy and finite-energy spectral properties of the model metallic phase.

UR - http://www.scopus.com/inward/record.url?scp=31944441171&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31944441171&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2005.12.016

DO - 10.1016/j.nuclphysb.2005.12.016

M3 - Article

VL - 737

SP - 237

EP - 260

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -