[PDF]     http://dx.doi.org/10.3952/lithjphys.52208

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 52, 165179 (2012)


LUTTINGER LIQUIDS WITH MULTIPLE FERMI EDGES: GENERALIZED FISHER-HARTWIG CONJECTURE AND NUMERICAL ANALYSIS OF TOEPLITZ DETERMINANTS
I.V. Protopopova,b, D.B. Gutmanc, and A.D. Mirlina,d,e
aInstitut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
E-mail: alexander.mirlin@kit.edu
bL.D. Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
cDepartment of Physics, Bar Ilan University, Ramat Gan 52900, Israel
dInstitut für Theorie der kondensierten Materie and DFG Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
ePetersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia

Received 28 March 2012; accepted 7 June 2012

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.
Keywords: non-equilibrium, many-body problems, Toeplitz determinants, Luttinger liquids, Fermi-edge singularity, tunneling spectroscopy
PACS: 73.23.-b, 73.40.Gk, 73.50.Td


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