Fluctuation Spectrum of Critical Fermi Surfaces

Abstract

We investigate the low-energy effective theory of a Fermi surface coupled to an Ising-nematic quantum critical point in (2+1) spacetime dimensions with translation symmetry. We formulate the system using the large $N$ Yukawa-SYK model, whose saddle point is described by the Migdal-Eliashberg equations. The low-energy physics can be revealed by studying the Gaussian fluctuation spectrum around the saddle point, which is generated by the Bethe-Salpeter kernel $K_{\text{BS}}$. Based on the Ward identities, we propose an inner product on the space of two point functions, which reveals a large number of soft modes of $K_{\text{BS}}$. These soft modes parameterize deformation of the Fermi surface, and their fluctuation eigenvalues describe their decay rates. We analytically compute these eigenvalues for a circular Fermi surface, and we discover the odd-parity modes to be parametrically longer-lived than the even-parity modes, due to the kinematic constraint of fermions scattering on a convex FS. The sign of the eigenvalues signals an instability of the Ising-nematic quantum critical point at zero temperature for a convex Fermi surface. At finite temperature, the system can be stabilized by thermal fluctuations of the critical boson. We derive an effective action that describes the soft-mode dynamics, and it leads to a linearized Boltzmann equation, where the real part of the soft-mode eigenvalues can be interpreted as the collision rates. The structure of the effective action is similar to the theory of linear bosonization of a Fermi surface. As an application, we investigate the hydrodynamic transport of non-Fermi liquid. Analyzing the Boltzmann equation, we obtain a conventional hydrodynamic transport regime and a tomographic transport regime. In both regimes, the conductance of the system in finite geometry can be a sharp indicator for the soft-mode dynamics and non-Fermi liquid physics.

53 pages, 7 figures; Part of the manuscript first appeared in arXiv:2311.03455 and arXiv:2311.03458. The current manuscript combines and expands the two previous manuscripts in a self-contained style with additional results; (v2) slightly updated abstract, discussion and reference; (v3) updated section VI; (v4) added clarification;

References in corpus (88)

• Anderson Transitions
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Negative local resistance caused by viscous electron backflow in graphene
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
• Inelastic Light Scattering From Correlated Electrons
• Quantum Theory of a Nematic Fermi Fluid
• Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
• Superballistic flow of viscous electron fluid through graphene constrictions
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Electron Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene
• Hydrodynamic electron flow in high-mobility wires
• Are non-Fermi-liquids stable to Cooper pairing?
• Low Energy Dynamics of the Spinon-Gauge System
• Hydrodynamic description of transport in strongly correlated electron systems
• Higher-Than-Ballistic Conduction of Viscous Electron Flows
• Theory of a continuous Mott transition in two dimensions
• Gauge-invariant response functions of fermions coupled to a gauge field
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Recent Developments in Non-Fermi Liquid Theory
• Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene
• Hydrodynamics in graphene: Linear-response transport
• Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal
• Quantum chaos on a critical Fermi surface
• Bulk and shear viscosities of the 2D electron liquid in a doped graphene sheet
• Eliashberg Theory: a short review
• Theory of a Planckian metal
• Non-analytic corrections to the Fermi-liquid behavior
• Collective cyclotron motion of the relativistic plasma in graphene
• Transport near the Ising-nematic quantum critical point of metals in two dimensions
• Universal theory of strange metals from spatially random interactions
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models
• Large $N$ theory of critical Fermi surfaces
• Magnetotransport in a model of a disordered strange metal
• Non-Fermi liquid behavior of large N_B quantum critical metals
• Resistivity of a non-Galilean--invariant Fermi Liquid near Pomeranchuk Quantum Criticality
• Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• Quantum Boltzmann equation of composite fermions interacting with a gauge field
• Critical Quadrupole Fluctuations and Collective Modes in Iron Pnictide Superconductors
• Superconductivity near a quantum-critical point: The special role of the first Matsubara frequency
• Anomalous dynamical scaling from nematic and U(1)-gauge field fluctuations in two dimensional metals
• Fermi liquid near Pomeranchuk quantum criticality
• Multidimensional Bosonization
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Linking Spatial Distributions of Potential and Current in Viscous Electronics
• Optical response of correlated electron systems
• Tomographic Dynamics and Scale-Dependent Viscosity in Two-Dimensional Electron Systems
• Chiral non-Fermi Liquids
• Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. I: The $\gamma$-model and its phase diagram at $T=0$. The case $0<\gamma <1$
• Quantum-critical pairing with varying exponents
• Two dimensional non-Fermi liquid metals: a solvable large N limit
• The Hierarchy of Excitation Lifetimes in Two-Dimensional Fermi Gases
• Spin conservation and Fermi liquid near a ferromagnetic quantum critical point
• Scattering mechanisms and electrical transport near an Ising nematic quantum critical point
• A critical strange metal from fluctuating gauge fields in a solvable random model
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Eliashberg equations for an electron-phonon version of the Sachdev-Ye-Kitaev model: Pair Breaking in non-Fermi liquid superconductors
• Quantum Phase Transition in the Yukawa-SYK Model
• Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal. II. The $\gamma$-model at a finite $T$ for $0<\gamma <1$
• Loop current fluctuations and quantum critical transport
• Normal state properties of quantum critical metals at finite temperature
• How non-Fermi liquids cure their infrared divergences
• Collective modes in interacting two-dimensional tomographic Fermi liquids
• Low temperature $T$-linear resistivity due to umklapp scattering from a critical mode
• Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data
• Fermion loops and improved power-counting in two-dimensional critical metals with singular forward scattering
• Manifestation of nematic degrees of freedom in the Raman response function of iron pnictides
• Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
• Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
• Anomalously long lifetimes in two-dimensional Fermi liquids
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids
• Fermi Surface Symmetric Mass Generation
• Non-Fermi-liquid behavior and anomalous suppression of Landau damping in layered metals close to ferromagnetism
• Cyclotron resonance and quantum oscillations of critical Fermi surfaces
• Specific Heat of a Quantum Critical Metal
• Zero sound and plasmon modes for non-Fermi liquids
• Collisionless dynamics of general non-Fermi liquids from hydrodynamics of emergent conserved quantities
• Thermal effects in non-Fermi liquid superconductivity
• Optical conductivity of a metal near an Ising-nematic quantum critical point
• Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point
• Controlled expansion for transport in a class of non-Fermi liquids
• An exact method for bosonizing the Fermi surface in arbitrary dimensions
• Fingerprints of quantum criticality in locally resolved transport
• Generic deformation channels for critical Fermi surfaces in the collisionless regime

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