Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography

Abstract

This note addresses the problem of computing fermion propagators in a broad variety of strongly correlated systems that can be mapped onto the theory of fermions coupled to an (over)damped bosonic mode. A number of the previously applied approaches and their results are reviewed, including the conventional diagrammatic resummation and eikonal technique, as well as the 'experimental' higher dimensional bosonization and generalized (i.e., 'bottom-up' or 'non-AdS/non-CFT') holographic conjecture. It appears that, by and large, those results remain either in conflict or incomplete, thereby suggesting that the ultimate solution to this ubiquitous problem is yet to be found.

Latex, 12 pages, few typos corrected

References in corpus (40)

• Lectures on Holographic Superfluidity and Superconductivity
• Effective Holographic Theories for low-temperature condensed matter systems
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Electron stars for holographic metallic criticality
• Large $N$ theory of critical Fermi surfaces
• Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions
• Scaling theory of the cuprate strange metals
• Dynamically Generated Gap from Holography: Mottness from a Black Hole
• Fermi surfaces and gauge-gravity duality
• Dynamical Gap and Cuprate-like Physics from Holography
• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Electrical resistivity near Pomeranchuk instability in two dimensions
• Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat
• A controlled expansion for certain non-Fermi liquid metals
• Composite Dirac fermions in graphene
• Luttinger's Theorem and Bosonization of the Fermi Surface
• Normal state properties of quantum critical metals at finite temperature
• Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals
• Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data
• Fermionic propagators for 2D systems with singular interactions
• The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions
• Lectures on quantum supreme matter
• Dirac fermions in a power-law-correlated random vector potential
• The Dirac composite fermion of the fractional quantum Hall effect
• Collective density fluctuations of strange metals with critical Fermi surfaces
• Statistical mechanics of strange metals and black holes
• Fermi Surface Resonance and Quantum Criticality in Strongly Interacting Fermi Gases
• Die Hard Holographic Phenomenology of Cuprates
• SYK does not Transit Gloria Mundi just yet
• Instabilities of quantum critical metals in the limit $N_f\to 0$
• Phase space holography with no strings attached
• Photoemission "experiments" on holographic lattices
• Holographic superconductivity of a critical Fermi surface
• Elusive gauge-invariant fermion propagator in QED-like effective theories: round II
• Exact Low-Energy Solution for Critical Fermi Surfaces

Cited by in corpus (2)

• Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities
• Marginal Fermi liquids from Fermi surfaces coupled via matrix boson gas