Non-fermi liquid and unconventional quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, both of which could occur in strongly interacting quantum many-body systems. This work demonstrates that using a controlled method one can construct a non-Fermi liquid within a considerable energy window based on the unique physics of unconventional QCPs. We will focus on the "nearly-marginal non-Fermi liquid", defined as a state whose fermion self-energy scales as $\Sigma_f(i \omega) \sim i \mathrm{sgn}(\omega)|\omega|^{\alpha}$ with $\alpha$ close to $1$ in a considerable energy window. The nearly-marginal non-fermi liquid is obtained by coupling an electron fermi surface to unconventional QCPs that are beyond the Landau's paradigm. This mechanism relies on the observation that the anomalous dimension $\eta$ of the order parameter of these unconventional QCPs can be close to $1$, which is significantly larger than conventional Landau phase transitions, for example the Wilson-Fisher fixed points. The fact that $\eta \sim 1$ justifies a perturbative renormalization group calculation proposed earlier. Various candidate QCPs that meet this desired condition are proposed.

中文翻译：

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非朗道量子相变和接近边缘的非费米液体

具有强分数化的非费米液体和非常规量子临界点 (QCP) 是超出经典凝聚态学说的两种特殊现象，这两种现象都可能发生在强相互作用的量子多体系统中。这项工作表明，基于非常规 QCP 的独特物理学，使用受控方法可以在相当大的能量窗口内构建非费米液体。我们将关注“接近边际的非费米液体”，定义为一种状态，其费米子自能缩放为 $\Sigma_f(i \omega) \sim i \mathrm{sgn}(\omega)|\omega| ^{\alpha}$ 与 $\alpha$ 在相当大的能量窗口中接近 $1$。通过将电子费米表面耦合到超出朗道范式的非常规 QCP 获得接近边缘的非费米液体。这种机制依赖于观察到这些非常规 QCP 的阶参数的异常维度 $\eta$ 可能接近 $1$，这明显大于传统的 Landau 相变，例如 Wilson-Fisher 固定点。$\eta \sim 1$ 证明了之前提出的微扰重整化群计算是合理的。提出了满足此所需条件的各种候选 QCP。