Holographic Effective Medium Theory

Understanding the anomalous transport properties of strange metals—such as those found in high-temperature superconductors—remains one of the central open problems in condensed matter physics. Holographic duality, originally developed in high-energy physics, can offer insights into these systems. By combining holographic models with ideas from effective medium theory (EMT), we investigate how nanoscale spatial inhomogeneity might influence the macroscopically observable transport properties such as the magnetoresistance.

In particular, we studied a quantum critical system subject to a spatially varying chemical potential, in the limit of strong translational symmetry breaking, and found that for 2D lattices, an “EMT” regime emerges naturally (Nilsson & Schalm, 2025). The electrical conductivity increases, as the current is able to take a curved path of least resistance through the potential landscape. This has implications for the magnetotransport, which exhibits a roughly B-linear dependence as seen in explicit EMT constructions. Furthermore, although our model has no coherent (Drude) conductivity on avergage, we observe the emergence of local Drude-ish hydrodynamics in each potential “pocket”, such that the total AC response exhibits typical “bad metal” behavior with a broad Drude peak.

References

arXiv
Quantum Critical Theories in a Periodic Potential: Strange Metallic Thermoelectric and Magnetotransport

Eric Nilsson and Koenraad Schalm

Dec 2025

Abs DOI Bib

We study DC and AC thermoelectric and magnetotransport in 2D quantum critical theories with strong translational symmetry breaking due to a varying chemical potential lattice with zero average \barμ=0. The combination of quantum criticality and the absence of the average natural scale implies that such systems have idiosyncratic signatures that may apply more generally when the variance in the lattice potential far exceeds the average or for strong translational symmetry breaking in general. We model such theories holographically through near-extremal AdS black holes. We find that these systems (a) become \emphbetter conductors. In a 2D lattice, this can be explained by currents flowing around obstacles; (b) exhibit bad-metal electrical transport with Drude-like thermal transport, though it is not Drude, and, notably, (c) display an approximately B-linear longitudinal magnetoresistance at large fields, similar to Effective Medium Theory. We comment on how these results may apply when \barμ≠0.
@misc{nilsson_quantum_2025, pubtype = {preprint}, title = {Quantum Critical Theories in a Periodic Potential: Strange Metallic Thermoelectric and Magnetotransport}, shorttitle = {Quantum Critical Theories in a Periodic Potential}, author = {Nilsson, Eric and Schalm, Koenraad}, year = {2025}, month = dec, number = {arXiv:2512.19480}, eprint = {2512.19480}, publisher = {arXiv}, doi = {10.48550/arXiv.2512.19480}, urldate = {2026-01-07}, archiveprefix = {arXiv}, }