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Physical review. B, Condensed matter

Analytical structure of the wave-number-dependent susceptibility of many-fermion systems at low temperature and long wavelength. II

D. J. W. Geldart, Mark Rasolt

Published Oct 15, 1980• 5 citations
Publisher

Abstract

For pt.I see ibid., vol.15, p.1523 (1977). It is shown that the nonanalytic structure of the wave-number-dependent susceptibility noted by Geldart and Rasolt is not removed by including repeated particle-particle scattering
DOI
10.1103/physrevb.22.4079

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The analytical structure of the wave-number-dependent magnetic susceptibility $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ is studied at small wave number $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ and low temperature. It is found to exhibit a nonanalytic behavior in contrast to commonly assumed forms for $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ of interacting systems. The importance and implications of these results are discussed for the cases of short-range point interactions and long-range Coulomb interactions.
Based on a second-order perturbation calculation with a $\ensuremath{\delta}$-function interaction, Geldart and Rasolt have recently shown that the long-wavelength static spin susceptibility is nonanalytic in TTT at low temperatures. We find the nonanalyticity is suppressed by the summation of particle-particle scattering terms to all orders. Commonly held analyticity assumptions regarding the long-wavelength and low-temperature behavior of the susceptibility are thus not invalidated. We suggest that for the nonuniform susceptibility, a Kohn-Luttinger-Ward-like equivalence between the zero- and low-temperature perturbation series exists between classes of terms, rather than order by order.
For pt.I see ibid., vol.10, p.2869 (1977). The local single-particle and density correlation functions for the symmetric Wolff model (1961) are studied in the asymptotic weak-coupling-long-time-low-temperature limit. The scattering channels are separated by means of the Stratonovich-Hubbard transformation and the associated one-body problem is solved explicitly in the low-temperature limit. A steepest-descent argument yields expressions for the correlation functions in the weak-coupling limit. The correlation functions are characterised by a time dependent phase shift which decays on a time scale of the order of the bandwidth. In the intermediate and strong coupling regime many-body effects intervene and the calculation breaks down; in that context comments are made on some recent work by Mattis (1976).