Yukawa-SYK model and self-tuned quantum criticality

Abstract

Non-Fermi liquids (NFLs) are a class of strongly interacting gapless fermionic systems without long-lived quasiparticle excitations. An important group of NFL models feature itinerant fermions coupled to soft bosonic fluctuations near a quantum-critical point 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 the Yukawa-SYK model). We show that it is immune from the 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 that 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 the test at finite N, and our unbiased numerics reveal clear evidence of these exotic quantum-critical NFL properties—the power-law behavior in the Green's function of fermions and bosons—which propels the theoretical understanding of critical Planckian metals and unconventional superconductors.