Planckian Metal at a Doping-Induced Quantum Critical Point

Abstract

We numerically study a model of interacting spin-1/2 electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi liquid with a large Fermi surface volume and a low-doping phase with local moments ordering into a spin-glass. We show that this quantum critical point has non-Fermi liquid properties characterized by T -linear Planckian behaviour, ω/T scaling and slow spin dynamics of the Sachdev-Ye-Kitaev (SYK) type. The ω/T scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a 'skewed' non Fermi liquid.

Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

“…For example when ImΣ = T ν f (ω/T ), we obtain ρ ∝ T ν ; ν = 1 corresponds to a Planckian metal. Evidence for such nFL behavior of the scattering rate was discussed above in the quantum critical regime of the random bond t-J and Hubbard models (Cha et al, 2020b;Dumitrescu et al, 2021). We also emphasize, as is well known from transport theory, that the wave function normalisation Z(T ) ∝ (1 − ∂ReΣ(ω, T )/∂ω| ω=0 ) −1 does not enter the expression of the conductivity, in contrast to the width of the one-electron spectral function which is ∝ Z|ImΣ| (and can be interpreted as the inverse of the quasiparticle lifetime in a Fermi liquid).…”

“…We will present numerical studies here (Dumitrescu et al, 2021;Otsuki and Vollhardt, 2013;Shackleton et al, 2021) showing that the spin glass order survives in a metallic state up to a critical doping p = p c , and that there is a Fermi liquid for p > p c . The critical point at p = p c displays a SYK-like criticality, with some similarities to the U = U c critical point at p = 0 described in Section VII.B.…”

“…A different and complementary approach (Otsuki and Vollhardt, 2013) was used recently (Dumitrescu et al, 2021). The EDMFT equations of Section VII.D were solved using the Quantum Monte Carlo algorithms reviewed in Section IX, corresponding to a direct solution in the thermodynamic limit N = ∞ for disorder-averaged observables.…”

“…The EDMFT equations of Section VII.D were solved using the Quantum Monte Carlo algorithms reviewed in Section IX, corresponding to a direct solution in the thermodynamic limit N = ∞ for disorder-averaged observables. The model considered (Dumitrescu et al, 2021) is actually a finite-U random exchange model, with U/t large enough so that the physics of a doped Mott insulating spin-glass is being captured. The phase diagram obtained in this study is displayed on Fig.…”

“…The metallic state is a Fermi liquid for p > p c , satisfying Luttinger theorem with a large Fermi energy associated with a fermion density of 1−p, see Section VIII.C for a discussion of the Luttinger theorem in disordered systems; for the present system, it is expressed by the relation µ−ReΣ(0) = ε F at T = 0, with ε F the Fermi energy of the non-interacting system (random matrix model) for a density n = 1−p. When solving the EDMFT equations without allowing for spin-glass ordering, a sudden breakdown of this relation is found for p < p c (Dumitrescu et al, 2021;Otsuki and Vollhardt, 2013), signalling a breakdown of the Luttinger theorem. These solutions correspond to a metastable state with unquenched local magnetic moments.…”