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arXiv:cond-mat/9908278 · Physical review. B, Condensed matter

Fermi-edge singularities in x-ray spectra of strongly correlated fermions

Dmitri V. Khveshchenko, Philip Warren Anderson

Published Jan 15, 2000• 5 citations
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Abstract

We discuss the problem of x-ray absorption in a D-dimensional system of interacting fermions and, in particular, those features in the x-ray spectra that can be used to discriminate between conventional Fermi liquids and ``strange metals.'' We find that the x-ray Fermi edge singularities can still be present, although modified, even if the density of states vanishes at the Fermi energy, and that, in general, the relationship between the two appears to be quite subtle.

DOI
10.1103/physrevb.61.1658

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We discuss the problem of x-ray absorption in a D-dimensional system of interacting fermions and, in particular, those features in the x-ray spectra that can be used to discriminate between conventional Fermi liquids and ``strange metals.'' We find that the x-ray Fermi edge singularities can still be present, although modified, even if the density of states vanishes at the Fermi energy, and that, in general, the relationship between the two appears to be quite subtle.
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Bosonization provides a powerful analytical framework to deal with one-dimensional strongly interacting fermion systems, which makes it a cornerstone in quantum many-body theory. However, this success comes at the expense of using effective infrared parameters, and restricting the description to low energy states near the Fermi level. We propose a radical extension of the bosonization technique that overcomes both limitations, allowing computations with microscopic lattice Hamiltonians, from the Fermi level down to the bottom of the band. The formalism rests on the simple idea of representating the fermion kinetic term in the energy domain, after which it can be expressed in terms of free bosonic degrees of freedom. As a result, one- and two-body fermionic scattering processes generate anharmonic boson−boson interactions, even in the forward channel. We show that up to moderate interaction strengths, these non-linearities can be treated analytically at all energy scales, using the x-ray emission problem as a showcase. In the strong interaction regime, we employ a systematic variational solution of the bosonic theory, and obtain results that agree quantitatively with an exact diagonalization of the original one-particle fermionic model. This provides a proof of the fully microscopic character of bosonization, on all energy scales, for an arbitrary band structure. Besides recovering the known x-ray edge singularity at the emission threshold, we find strong signatures of correlations even at emission frequencies beyond the band bottom.