Locally critical umklapp scattering and holography

TL;DR

The paper shows that local quantum criticality provides a distinct mechanism for momentum relaxation via umklapp scattering, yielding a dc resistivity that scales as Γ ∼ T^{2Δ_kL} where Δ_kL is the IR scaling dimension of the finite-momentum charge density operator J^t at the lattice momentum. Using memory-matrix techniques, it derives a general formula for Γ controlled by the density-density spectral function at the lattice momentum, and then anchors the idea in a concrete holographic model with AdS2×R^2 IR geometry. In the holographic context, Γ ∼ T^{2ν_-−1} with ν_- set by k_L, reproducing the predicted T-power and linking it to a dimensionless momentum scale; the work also discusses universal impurity scattering and extensions to finite-z critical theories. Overall, it provides a holographic realization of locally critical umklapp scattering and highlights potential universal behavior in dc transport beyond Fermi-surface-based mechanisms.

Abstract

Efficient momentum relaxation through umklapp scattering, leading to a power law in temperature d.c. resistivity, requires a significant low energy spectral weight at finite momentum. One way to achieve this is via a Fermi surface structure, leading to the well-known relaxation rate Gamma ~ T^2. We observe that local criticality, in which energies scale but momenta do not, provides a distinct route to efficient umklapp scattering. We show that umklapp scattering by an ionic lattice in a locally critical theory leads to Gamma ~ T^(2Δ(k_L)). Here Δ(k_L) \geq 0 is the dimension of the (irrelevant or marginal) charge density operator J^t(w,k_L) in the locally critical theory, at the lattice momentum k_L. We illustrate this result with an explicit computation in locally critical theories described holographically via Einstein-Maxwell theory in Anti-de Sitter spacetime. We furthermore show that scattering by random impurities in these locally critical theories gives a universal Gamma ~ 1/log(1/T)

Figures (1)

• Figure 1: Temperature power law of the d.c. resistivity as a function of the lattice momentum $k_L$ in models with an Einstein-Maxwell gravity dual. The physical normalization of the momentum depends on the UV completion of the locally critical theory.