Yukawa-SYK model and self-tuned quantum criticality
Yukawa-SYK model and self-tuned quantum criticality
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DOI：
10.1103/physrevresearch.3.013250
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
Gaopei Pan;Wei Wang;A. Davis;Yuxuan Wang;Z. Meng
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文献类型：
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作者：
Gaopei Pan;Wei Wang;A. Davis;Yuxuan Wang;Z. Meng
非费米液体（NFL）是一类没有长寿命准粒子激发的强相互作用无带隙费米系统。NFL模型的一个重要组成部分是在量子临界点（QCP）附近耦合到软玻色子波动的巡回费米子，并且被广泛认为可以捕获许多非常规超导体的基本物理。然而，在这种系统中，典型的NFL行为，其特征在于在绿色函数的幂律形式的直接观察，一直难以捉摸。在这里，我们考虑一个Sachdev-Ye-Kitaev（SYK）类模型与临界玻色子和费米子之间的随机汤川相互作用（称为汤川-SYK模型）。我们表明，它是免疫的负符号问题，因此可以通过大规模量子蒙特卡罗模拟超出了大$N$限制解析方法精确地解决。我们的模拟表明Yukawa-SYK模型具有“自调谐量子临界性”，即系统是临界的，与玻色子裸质量无关。我们把这些结果测试在有限的$N$，我们的无偏数值揭示了这些外来的量子临界NFL属性的明确证据-幂律行为在绿色的费米子和玻色子的功能-这推动了临界普朗克金属和非常规超导体的理论理解。
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.