Luttinger liquids with multiple fermi edges: Generalized fisher-hartwig conjecture and numerical analysis of toeplitz determinants

I. V. Protopopov, D. B. Gutman, A. D. Mirlin

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

It has been shown that solutions of a number of many-body problems out of equilibrium can be expressed in terms of Toeplitz determinants with Fisher-Hartwig (FH) singularities. In the present paper, such Toeplitz determinants are studied numerically. Results of our numerical calculations fully agree with the FH conjecture in an extended form that includes a summation over all FH representations (corresponding to different branches of the logarithms). As specific applications, we consider problems of Fermi edge singularity and tunneling spectroscopy of Luttinger liquid with multiple-step energy distribution functions, including the case of population inversion. In the energy representation, a sum over FH branches produces power-law singularities at multiple edges.

Original languageEnglish
Pages (from-to)165-179
Number of pages15
JournalLithuanian Journal of Physics
Volume52
Issue number2
DOIs
StatePublished - 2012

Bibliographical note

Invited paper honoring the memory of Yehoshua Levinson

Keywords

  • Fermi-edge singularity
  • Luttinger liquids
  • Many-body problems
  • Non-equilibrium
  • Toeplitz determinants
  • Tunneling spectroscopy

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