Using a previously derived effective theory we explore the conductance in the Luttinger model with one impurity. A new approach to the renormalization group (RG) analysis of this model is developed. It is based on the original Gell-Mann-Low formulation of RG. We sum up infrared logarithmic contributions to conductance in the leading and a few subsequent approximations. We analyze the validity of the widely used 'poor man's' scaling approach and find that it is applicable only in the leading approximation. Our results for corrections to this approximation are different from results obtained in other papers. This should be expected beforehand, as the Gell-Mann-Low function of the model is not regularization scheme invariant. For this reason the observed quantity (e.g. conductance) can not satisfy the Gell-Mann-Low equation beyond the 'leading-log' approximation as it is supposed in the 'poor man's' approach. We formulate the method to calculate the conductance from the renormalized hamiltonian in post-leading approximations and match our results to the case of weak impurity where the answer is known in any order of electron-electron interaction.Using a previously derived effective theory we explore the conductance in the Luttinger model with one impurity. A new approach to the renormalization group (RG) analysis of this model is developed. It is based on the original Gell-Mann-Low formulation of RG. We sum up infrared logarithmic contributions to conductance in the leading and a few subsequent approximations. We analyze the validity of the widely used 'poor man's' scaling approach and find that it is applicable only in the leading approximation. Our results for corrections to this approximation are different from results obtained in other papers. This should be expected beforehand, as the Gell-Mann-Low function of the model is not regularization scheme invariant. For this reason the observed quantity (e.g. conductance) can not satisfy the Gell-Mann-Low equation beyond the 'leading-log' approximation as it is supposed in the 'poor man's' approach. We formulate the method to calculate the conductance from the renormalized hamiltonian in post-leading approximations and match our results to the case of weak impurity where the answer is known in any order of electron-electron interaction.

arXiv:1604.04704Journal of Physics Condensed MatterJul 23, 20182 citations

Renormalization group approach to the phase diagram of two-dimensional Heisenberg spin systems

José G. Esteve, Amalio F. Pacheco

Nuclear Physics BOct 1, 19792 citations

Renormalization group for one-dimensional Fermi systems: Three-loop scaling equations

Edward H. Rezayi, Josef Sak, S. Talukdar

The one-dimensional Fermi system with Tomonaga-type ( ${g}_{2}$ ) and back-scattering ( ${g}_{1}$ ) interactions is studied by a weak-coupling renormalization-group method at the three-loop level. When the transfer cutoff procedure is used, the Gell-Mann-Low function for ${g}_{1}$ depends on ${g}_{1}$ alone, $\frac{d{g}_{1}}{d\ensuremath{\xi}}={{g}_{1}}^{2}+\frac{1}{2}{{g}_{1}}^{3}+\frac{1}{8}{{g}_{1}}^{4}$. Further, in the absence of umklapp processes the combination ${g}_{1}\ensuremath{-}2{g}_{2}$ is a scale invariant. These conclusions agree with the results of Luther and Emery derived by the boson representation method. Some novel calculational techniques for the derivation of the scaling equations are described and compared to the conventional scheme.The one-dimensional Fermi system with Tomonaga-type (${g}_{2}$) and back-scattering (${g}_{1}$) interactions is studied by a weak-coupling renormalization-group method at the three-loop level. When the transfer cutoff procedure is used, the Gell-Mann-Low function for ${g}_{1}$ depends on ${g}_{1}$ alone, $\frac{d{g}_{1}}{d\ensuremath{\xi}}={{g}_{1}}^{2}+\frac{1}{2}{{g}_{1}}^{3}+\frac{1}{8}{{g}_{1}}^{4}$. Further, in the absence of umklapp processes the combination ${g}_{1}\ensuremath{-}2{g}_{2}$ is a scale invariant. These conclusions agree with the results of Luther and Emery derived by the boson representation method. Some novel calculational techniques for the derivation of the scaling equations are described and compared to the conventional scheme.

Physical review. B, Condensed matterMay 1, 197912 citations

Renormalization group treatment of quantum Heisenberg model

I. Golhirsch, Evgeny Levich, Victor Yakhot

Jan 1, 19770 citations

The one-dimensional Fermi system with Tomonaga-type (

{g}_{2}

) and back-scattering (

{g}_{1}

) interactions is studied by a weak-coupling renormalization-group method at the three-loop level. When the transfer cutoff procedure is used, the Gell-Mann-Low function for

{g}_{1}

depends on

{g}_{1}

alone, $\frac{d{g}_{1}}{d\ensuremath{\xi}}={{g}_{1}}^{2}+\frac{1}{2}{{g}_{1}}^{3}+\frac{1}{8}{{g}_{1}}^{4}$. Further, in the absence of umklapp processes the combination ${g}_{1}\ensuremath{-}2{g}_{2}$ is a scale invariant. These conclusions agree with the results of Luther and Emery derived by the boson representation method. Some novel calculational techniques for the derivation of the scaling equations are described and compared to the conventional scheme.