Heat bath approach to Landau damping and Pomeranchuk quantum critical points

We study the problem of the damping of collective modes close to a Pomeranchuk quantum critical point in a Fermi liquid. In analogy with problems in dissipative open quantum systems, we derive the Landau damping of a Fermi liquid by integrating out a macroscopic number of degrees of freedom from a generating functional. Being a reformulation of the linearized Boltzmann equation, this approach reproduces well-known results from the theory of Fermi liquids. We also study the Bethe-Salpeter equations within the Landau theory and discuss the implications of these results on quantum phase transitions of the Pomeranchuk type and its dynamical exponent, $z$. We apply our results to the electronic nematic instability and find $z=3$ in the collisionless limit.

Figure 1

(Color online) Phase diagram of a quantum critical Pomeranchuk instability of order $m$. Vertical axis: temperature $T$; horizontal axis: Landau parameter $F_m$. The dashed arrow line shows the direction of approach to the quantum critical point used in this work.