Strange metals as ersatz Fermi liquids

TL;DR

This paper investigates the fundamental conditions under which translation invariant metals can exhibit non-Fermi liquid behavior with linear resistivity and $/T$ scaling, revealing intrinsic properties of low energy fixed points.

Contribution

It demonstrates that such non-Fermi liquid metals must have a diverging susceptibility for certain operators and discusses the implications for experimental observations and exotic phenomena.

Findings

Linear resistivity arises from low energy fixed point physics.

Diverging susceptibility for operators odd under inversion/time reversal.

Potential for other exotic phenomena due to loopholes.

Abstract

A long standing mystery of fundamental importance in correlated electron physics is to understand strange non-Fermi liquid metals that are seen in diverse quantum materials. A striking experimental feature of these metals is a resistivity that is linear in temperature ($T$). In this paper we ask what it takes to obtain such non-Fermi liquid physics down to zero temperature in a translation invariant metal. If in addition the full frequency ($\omega$) dependent conductivity satisfies $\omega/T$ scaling, we argue that the $T$-linear resistivity must come from the intrinsic physics of the low energy fixed point. Combining with earlier arguments that compressible translation invariant metals are `ersatz Fermi liquids' with an infinite number of emergent conserved quantities, we obtain powerful and practical conclusions. We show that there is necessarily a diverging susceptibility for an operator that is odd under inversion/time reversal symmetries, and has zero crystal momentum. We discuss a few other experimental consequences of our arguments, as well as potential loopholes which necessarily imply other exotic phenomena.