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arXiv:1504.05504 · The European Physical Journal B

Conserving approximations for response functions of the Fermi gas in a random potential

V. Janiš, Jindřich Kolorenč

Published Jul 1, 2016• 2 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2016-70188-1

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The response functions of the one-dimensional Fermi gas with backscattering are studied using an equivalence of the spin-density part of the Fermi Hamiltonian to the sine-Gordon Hamiltonian. The singlet spin-density response function is evaluated in functional-integral form, using a transfer-matrix technique. For low temperatures and large distances, this function is found to be unity. The triplet response function is found, in a harmonic approximation, to be zero. These results support the proposal by Luther and Emery that the singular behavior of the Fermi-gas response functions is determined solely by the charge-density modes. Also supported is the rather intuitive picture, based on a mapping to the two-dimensional Coulomb gas, of Chui and Lee.