Holographic Metals and Insulators with Helical Symmetry

TL;DR

<3-5 sentence high-level summary>We address finite-density strongly coupled systems using holography by constructing homogeneous, zero-temperature scaling solutions with helical (Bianchi VII$_0$) symmetry in a 5D Einstein-Maxwell-Dilaton theory with two U(1) gauge fields. The authors derive a general DC conductivity formula from horizon data and compute the low-frequency AC conductivity via matched asymptotics, revealing a rich landscape of anisotropic insulating and conducting phases as well as isotropic metals, with transport controlled either by momentum dissipation or quantum critical currents. They classify IR saddles into anisotropic and isotropic families, including marginal and irrelevant density deformations and partially hyperscaling-violating limits, and identify parameter regimes yielding metal-insulator transitions that resemble phenomena in strongly correlated materials. The results provide a controlled holographic framework to study how translation symmetry breaking and density deformations shape transport in quantum critical systems, with potential relevance to cuprates and other anisotropic conductors.

Abstract

Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in Einstein-Maxwell-Dilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming $AdS_{5}$ UV asymptotics, the small frequency/(temperature) dependence of the AC/(DC) electric conductivity along the director of the helix are computed. A large class of insulating and conducting anisotropic phases is found, as well as isotropic, metallic phases. Conduction can be dominated by dissipation due to weak breaking of translation symmetry or by a quantum critical current.