Abstract
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 non-perturbative 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 is absent from the zero temperature critical point. 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.
Highlights
Ized by the destruction of the quasi-particle spectrum, and the resulting non-fermi-liquid-like transport and thermodynamic properties[6,7,8,9]
We will focus on the behavior of quantum critical metals at finite temperature in their normal state
T = 0 scalings have often been assumed to be valid near quantum critical points; the violation we find here means that aspects of transport and superconductivity in non-Fermi liquids (NFLs) will have to be reconsidered
Summary
Let us review the class of NFLs that will be studied in the rest of the work These arise from metals near a symmetry breaking transition at zero momentum. As we review below, the boson inherits its dynamics from fermionic quantum effects (the Landau damping function), and this dominates at low energies over a possible tree level term with time derivatives. It is natural to ask whether the approximation of rainbow resummation holds for finite N , which would be relevant for real NFLs. For this, we note that all corrections to the fermion Green’s functions that we neglect when N → ∞ arise from loop corrections to the cubic vertex φψψ; see e.g. Fig. 2 b) below. We will uncover a new “thermal” NFL regime that arises for euclidean frequencies ω ∼ πT , or real frequencies p0 T
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