Lifshitz Hydrodynamics

TL;DR

This work develops a hydrodynamic description for quantum critical points with Lifshitz scaling, where boost invariance is explicitly broken. It identifies a single new dissipative coefficient $α$, derives the Lifshitz algebra, and formulates the energy–momentum tensor and Ward identities, including the nonrelativistic limit to a Galilean fluid. In a Drude-like model for strange metals, the leading conductivity is $\bm{σ}= (\rho/λ) I$ with a Planckian drag time $λ$, yielding a linear-in-$T$ resistivity $ρ \propto T$ that is independent of the dynamical exponent $z$ and spatial dimension $d$, while the coefficient $α$ introduces field-gradient dependent corrections and a dissipative heat term $ΔQ$. Overall, the paper provides a universal, boost-breaking hydrodynamic framework with testable transport and dissipation signatures in Lifshitz-critical systems and related media.

Abstract

We construct the hydrodynamics of quantum critical points with Lifshitz scaling. There are new dissipative effects allowed by the lack of boost invariance. The formulation is applicable, in general, to any fluid with an explicit breaking of boost symmetry. We use a Drude model of a strange metal to study the physical effects of the new transport coefficient. It can be measured using electric fields with non-zero gradients, or via the heat production when an external force is turned on. Scaling arguments fix the resistivity to be linear in the temperature.

Figures (1)

• Figure 1: Valid region of hydrodynamic description of quantum critical point (QCP). $T$ is a temperature and $P$ is a quantum tuning parameter.