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arXiv · 2001.06586

Yukawa-SYK model and Self-tuned Quantum Criticality

Gaopei Pan·Wei Wang·Andrew Davis·Yuxuan Wang·Zi Yang Meng
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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.

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Gaopei Pan, Wei Wang, Andrew Davis, Yuxuan Wang, Zi Yang Meng. 2020-01-18. Yukawa-SYK model and Self-tuned Quantum Criticality. https://doi.org/10.1103/physrevresearch.3.013250

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