Loop current fluctuations and quantum critical transport

Abstract

We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the "Hertz-Millis" type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving $N$ species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, $\sigma (\omega >0)\sim {\omega }^{-2/z}$, where $z$ is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large $N$ expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical $N=1$ system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, $\sigma (\omega >0)\sim {\omega }^{-2(z-2)/z}$, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.

36 pages + 35 pages appendices. v2 updated to match published version

References in corpus (21)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum Criticality in Heavy Fermion Metals
• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Are non-Fermi-liquids stable to Cooper pairing?
• Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
• Theory of a continuous Mott transition in two dimensions
• Quantum chaos on a critical Fermi surface
• Theory of the Quantum Critical Fluctuations in Cuprates
• Large $N$ theory of critical Fermi surfaces II: conductivity
• 2D orbital-like magnetic order in $\mathrm{L}{\mathrm{a}}_{2-\mathrm{x}}\mathrm{S}{\mathrm{r}}_{\mathrm{x}}\mathrm{Cu}{\mathrm{O}}_4$
• A controlled expansion for certain non-Fermi liquid metals
• Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• No Evidence for Orbital Loop Currents in Charge Ordered YBa${}_2$Cu${}_3$O${}_{6+x}$ from Polarized Neutron Diffraction
• How non-Fermi liquids cure their infrared divergences
• Thermodynamic Properties near the onset of Loop-Current Order in high-$T_c$ superconducting cuprates
• Local Quantum Criticality in the Two-dimensional Dissipative Quantum XY Model
• Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions
• Long Wavelength Correlations and Transport in a Marginal Fermi Liquid
• Quantum-critical resistivity of strange metals in a magnetic field

Cited by in corpus (30)

• Universal theory of strange metals from spatially random interactions
• Strange metal and superconductor in the two-dimensional Yukawa-Sachdev-Ye-Kitaev model
• Theory of shot noise in strange metals
• Non-Fermi liquids from kinetic constraints in tilted optical lattices
• Cyclotron resonance and quantum oscillations of critical Fermi surfaces
• Solvable models of two-level systems coupled to itinerant electrons: Robust non-Fermi liquid and quantum critical pairing
• Optical conductivity of a metal near an Ising-nematic quantum critical point
• Collisionless dynamics of general non-Fermi liquids from hydrodynamics of emergent conserved quantities
• Strange metals and black holes: insights from the Sachdev-Ye-Kitaev model
• Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point
• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
• Non-Fermi Liquids from Dipolar Symmetry Breaking
• A Criterion for Strange Metallicity in the Lorenz Ratio
• Controlled expansion for transport in a class of non-Fermi liquids
• Fluctuation Spectrum of Critical Fermi Surfaces
• Holographic models of non-Fermi liquid metals revisited: an effective field theory approach
• Conductance and thermopower fluctuations in interacting quantum dots
• Effective field theory for ersatz Fermi liquids
• Linear-T Resistivity from Spatially Random Vector Coupling
• Fractionalized Fermi liquids and the cuprate phase diagram
• Strong-coupling superconductivity near Gross-Neveu quantum criticality in Dirac systems
• Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction
• Fermi Surface Bosonization for Non-Fermi Liquids
• Hall Angle of a Spatially Random Vector Model
• Magnetoconductivity due to electron-electron interaction in a non-Galilean-invariant Fermi liquid
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
• Phonon Induced Energy Relaxation in Quantum Critical Metals
• Strange metal in the doped Hubbard model via percolation
• Can electronic quantum criticality drive phonon-induced linear-in-temperature resistivity?
• Marginal Fermi liquids from Fermi surfaces coupled via matrix boson gas