Quantum discontinuity fixed point and renormalization group flow of the Sachdev-Ye-Kitaev model,Physical Review Research

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Quantum discontinuity fixed point and renormalization group flow of the Sachdev-Ye-Kitaev model
Physical Review Research ( IF 3.5 ) Pub Date : 2021-07-23 , DOI: 10.1103/physrevresearch.3.033089
Roman Louis Smit ₁ , Davide Valentinis _{2,

3} , Jörg Schmalian _{2,

3} , Peter Kopietz ₁

Affiliation

We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. From a controlled truncation of the infinite hierarchy of the exact functional RG flow equations, we identify several fixed points. Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum first-order transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of the transition in terms of a local effective Ising variable as is established for classical transitions. We propose an entangled quantum state at phase coexistence as a possible physical origin of this critical behavior.

中文翻译：

Sachdev-Ye-Kitaev 模型的量子不连续不动点和重整化群流

我们确定 Sachdev-Ye-Kitaev (SYK) 模型的全局重整化群 (RG) 流。从精确函数 RG 流动方程的无限层次的受控截断，我们确定了几个固定点。除了与模型著名的非费米液态相关的稳定不动点外，我们还发现了另一个与整数价态相关的稳定不动点。这些稳定的不动点被一个具有一个相关方向的不连续不动点隔开，描述了量子一阶跃迁。最值得注意的是，即使在不连续性固定点，费米子光谱仍然是量子临界的。这排除了根据为经典转换建立的局部有效 Ising 变量的转换描述。

更新日期：2021-07-24

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