Dynamical susceptibility of a Fermi liquid

Abstract

We study dynamic response of a Fermi liquid in the spin, charge and nematic channels beyond the random phase approximation for the dynamically screened Coulomb potential. In all the channels, one-loop order corrections to the irreducible susceptibility result in a non-zero spectral weight of the corresponding fluctuations above the particle-hole continuum boundary. It is shown that the imaginary part of the spin susceptibility, Imχs(q, ω), falls off as q 2 /ω for frequencies above the continuum boundary (ω vFq) and below the model-dependent cutoff frequency, whereas the imaginary part of the charge susceptibility, Imχc(q, ω), falls off as (q/kF ) 2 q 2 /ω for frequencies above the plasma frequency. An extra factor of (q/kF ) 2 in Imχc(q, ω) as compared to Imχs(q, ω) is a direct consequence of Galilean invariance. The imaginary part of the nematic susceptibility increases linearly with ω up to a peak at the ultraviolet energy scale-the plasma frequency and/or Fermi energy-and then decreases with ω. We also obtain explicit forms of the spin susceptibility from the kinetic equation in the collisionless limit and for the Landau function that contains up to first three harmonics. arXiv:1806.10159v1 [cond-mat.str-el]

Collective spinon spin wave in a magnetized U(1) spin liquid

“…Importantly, the "result" is seemingly independent of a momentum cut-off even though the intermediate steps do require an explicit cut-off of the order k F when integrating over gauge momentum p ⊥ . Carrying out the frequency integration first, similar to the calculations in Maslov et al [36], produces quite a different answer…”

Optical conductivity of a Dirac-Fermi liquid

“…Also, the matrix elements in the Green functions for doped graphene can be replaced by unities in the forward-scattering limit. Under these approximations, the sum of the three diagrams can be written as [60]…”

Collective modes near a Pomeranchuk instability in two dimensions

“…The behavior of the full susceptibility is then determined entirely by the quasiparticle χ c(s) qp,l (q, ω). Although the calculations are straightforward and some of the results have appeared before, 26,28,[30][31][32][33][34][35][36][37][38][39][40] we include below the details of the derivation of χ c(s) qp,l (q, ω) in 2D, as we will be interested in the pole structure of the susceptibility not only near a Pomeranchuk transition but also away from it. In what follows we consider separately the cases of l = 0, 1, 2, and then analyze the case of arbitrary l. In these calculations we assume that a single Landau parameter F c(s) l is much larger than the rest and compute χ c(s) qp,l (q, ω) using Eq.…”

“…l = 1, longitudinalWe start with recalling the situation at vanishingly small damping. For −1 < F c(s) 1 < 0, the poles of χ long qp,1 (s) are at s 1,2 = ±a 1 − ib 1 , where a 1 and b 1 are given by Eq (35)…”