Renormalization group flows in one-dimensional lattice models: Impurity scaling, umklapp scattering, and the orthogonality catastrophe

D. M. Kennes, M. J. Schmidt, D. Hübscher, and V. Meden
Phys. Rev. B 90, 155129 – Published 27 October 2014

Abstract

We show that to understand the orthogonality catastrophe in the half-filled lattice model of spinless fermions with repulsive nearest-neighbor interaction and a local impurity in its Luttinger liquid phase one has to take into account (i) the impurity scaling, (ii) unusual finite-size L corrections of the form ln(L)/L, as well as (iii) the renormalization group flow of the umklapp scattering. The latter defines a length scale Lu, which becomes exceedingly large the closer the system is to its transition into the charge density wave phase. Beyond this transition umklapp scattering is relevant in the renormalization group sense. Field theory can only be employed for length scales larger than Lu. For small to intermediate two-particle interactions, for which the regime L>Lu can be accessed, and taking into account the finite-size corrections resulting from (i) and (ii) we provide strong evidence that the impurity backscattering contribution to the orthogonality exponent is asymptotically given by 1/16. While further increasing the two-particle interaction leads to a faster renormalization group flow of the impurity towards the cut chain fixed point, the increased bare amplitude of the umklapp scattering renders it virtually impossible to confirm the expected asymptotic value of 1/16 given the accessible system sizes. We employ the density matrix renormalization group.

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  • Received 5 September 2014
  • Revised 8 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.155129

©2014 American Physical Society

Authors & Affiliations

D. M. Kennes1, M. J. Schmidt2, D. Hübscher2, and V. Meden1

  • 1Institut für Theorie der Statistischen Physik, RWTH Aachen University and JARA - Fundamentals of Future Information Technology, 52056 Aachen, Germany
  • 2Institut für Theoretische Festkörperphysik, RWTH Aachen University, 52056 Aachen, Germany

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Vol. 90, Iss. 15 — 15 October 2014

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