Non-Fermi liquids at finite temperature: Normal-state and infrared singularities

We analyze quantum criticality at finite temperature for a class of non-Fermi liquids with massless bosons. Finite temperature gives rise to new infrared singularities that invalidate standard perturbative treatments. We show how such divergences are resolved at a nonperturbative level, and obtain the resulting fermion self-energy. This leads to a new “thermal” non-Fermi liquid regime that extends over a wide range of frequencies, and which violates finite temperature scaling laws near quantum critical points. We analyze the resulting quantum critical region and properties of the retarded Green's function. More generally, such effects dominate in the nearly static limit and are expected to have a nontrivial impact on superconductivity and transport.

Figure 1

Schematic phase diagram around a quantum critical point for coupling $g=g_c$. The quantum critical region (QCR) occurs for $kT>\mathrm{\Delta }$, with $\mathrm{\Delta }$ the typical mass scale for $g\ne g_c$.

Figure 2

Two-loop corrections to the fermion and boson self-energy. (b) and (d) Subleading at large $N$.

Figure 3

Schwinger-Dyson equations for the fermion and boson self-energy in the large $N$ theory.

Figure 4

Left panel: Exact solution to (4.8) (red), approximate solution (4.12) (blue), and NFL answer ignoring the thermal piece (black). Parameters: $\epsilon =0.3,\alpha =\epsilon /3,\pi T={10}^{-5}$. Right panel: Evolution of $\mathrm{\Sigma }\left(\pi T\right)$ as a function of $T$ for $\epsilon =0.3$ (black), $\epsilon =0.5$ (blue), $\epsilon =1$ (red).

Figure 5

Phase structure of the quantum critical region near a NFL fixed point.