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

P. Anderson, Dmitri V. Khveshchenko

Published May 5, 2023• 0 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
10.17615/r24k-b071

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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.
We study the singularities in x-ray absorption spectra of one-dimensional Hubbard and ttt-JJJ models. We use boundary conformal field theory and the Bethe ansatz solutions of these models with both periodic and open boundary conditions to calculate the exponents describing the power-law decay near the edges of x-ray absorption spectra in the case where the core-hole potential has bound states.
Modern condensed matter physics owes much of its success to Fermi liquid theory. In recent times, however, the study of strongly correlated particle systems is opening up all-new territory in many-body physics. A peculiar class of such systems, that of nodal fermions, is characterized by the quasiparticle density of states vanishing at the point-like Fermi surface and long-range inter-particle interactions surviving unscreened. In the first part, I discuss fermion pairing in one such system, 2D graphene. By solving the gap equation for the excitonic order parameter, I obtain values of critical interaction strength for a variety of power-law interactions and densities of states. Furthermore, these results are then used to compute the respective free energies and analyze possible phase transitions. In the second part, I discuss the effects of lattice disorder and impurities on the density of states in nodal fermion systems. These results and predictions will be of interest to a broad range of physical problems involving nodal fermions, and can be tested in a variety of experimental directions.
An introductory survey of the theoretical ideas and calculations and experimental results which depart from Landau Fermi liquids is presented. The common themes and possible routes to the singularities leading to breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Soluble examples of singular or Non Fermi‐liquids include models of impurities in metals with special symmetries and one‐dimensional interacting fermions. A review of these is followed by a discussion of singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low energy collective fluctuations, gauge fields, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two dimensional metallic state.