Yukawa-SYK model and Self-tuned Quantum Criticality

Abstract

Non-Fermi liquids (NFL) are a class of strongly interacting gapless fermionic systems without long-lived quasiparticle excitations. An important group of NFL model features itinerant fermions coupled to soft bosonic fluctuations near a quantum-critical point (QCP), and are widely believed to capture the essential physics of many unconventional superconductors. However numerically the direct observation of a canonical NFL behavior in such systems, characterized by a power-law form in the Green's function, has been elusive. Here we consider a Sachdev-Ye-Kitaev (SYK)-like model with random Yukawa interaction between critical bosons and fermions (dubbed Yukawa-SYK model). We show it is immune from minus-sign problem and hence can be solved exactly via large-scale quantum Monte Carlo simulation beyond the large-$N$ limit accessible to analytical approaches. Our simulation demonstrates the Yukawa-SYK model features "self-tuned quantum criticality", namely the system is critical independent of the bosonic bare mass. We put these results to test at finite $N$, and our unbiased numerics reveal clear evidence of these exotic quantum-critical NFL properties -- the power-law behavior in Green's function of fermions and bosons -- which propels the theoretical understanding of critical Planckian metals and unconventional superconductors.

arXiv comment13 pages, 8 figures

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Cited by in corpus (24)

• Large $N$ theory of critical Fermi surfaces
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Phase diagram of the spin-1/2 Yukawa-SYK model: Non-Fermi liquid, insulator, and superconductor
• Superconductivity of incoherent electrons in Yukawa-SYK model
• Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
• Quantum Monte Carlo Simulation of Generalized Kitaev Models
• Quantum chaos and phase transition in the Yukawa-SYK model
• Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence
• Fermi arcs and pseudogap in a lattice model of a doped orthogonal metal
• A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Symmetry breaking in zero-field two-dimensional electron bilayers
• SYK does not Transit Gloria Mundi just yet
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• $\mathcal{N}=2$ SYK models with dynamical bosons and fermions
• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• High-Temperature Superconductivity from Finite-Range Attractive Interaction
• Non-Fermi liquid fixed point of the dissipative Yukawa-Sachdev-Ye-Kitaev model
• Upper bound on $T_c$ in a strongly coupled electron-boson superconductor
• Negative sign free formulations of generalized Kitaev models with higher symmetries
• Universal quench dynamics of lattice $q$ fermion Yukawa Sachdev-Ye-Kitaev model
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal