Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals

Abstract

Superconductivity is abundant near quantum-critical points, where fluctuations suppress the formation of Fermi liquid quasiparticles and the BCS theory no longer applies. Two very distinct approaches have been developed to address this issue: quantum-critical Eliashberg theory and holographic superconductivity. The former includes a strongly retarded pairing interaction of ill-defined fermions, the latter is rooted in the duality of quantum field theory and gravity theory. We demonstrate that both are different perspectives of the same theory. We derive holographic superconductivity in form of a gravity theory with emergent space-time from a quantum many-body Hamiltonian - the Yukawa SYK model - where the Eliashberg formalism is exact. Exploiting the power of holography, we then determine the dynamic pairing susceptibility of the model. Our holographic map comes with the potential to use quantum gravity corrections to go beyond the Eliashberg regime.

10 pages, 4 figures

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• Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
• Superconductor--Insulator Transition in a non-Fermi Liquid
• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• Investigating quantum criticality through charged scalar fields near the BTZ black hole horizon
• Electric conductivity in non-Hermitian holography
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• Quantum Speed Limits from Symmetries in Quantum Control
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Triplet pairing, orbital selectivity and correlations in Iron-based superconductors
• Instabilities of a Generalized Gross-Neveu Quantum Criticality
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
• Odd-frequency superfluidity from a particle-number-conserving perspective
• Universal quench dynamics of lattice $q$ fermion Yukawa Sachdev-Ye-Kitaev model