论文标题
Sachdev-ye-Kitaev模型的精确低温扩展
Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model
论文作者
论文摘要
我们从数字上求解了使用Legendre多项式分解并达到$ 10^{ - 36} $精度的Sachdev-Ye-Kitaev（Syk）型号的大型$ n $ dyson-schwinger方程。使用此，我们计算低温下Syk模型的能量，并将其系列扩展达到$ t^{7.54} $。虽然建议扩展包含术语$ t^{3.77} $和$ t^{5.68} $，但我们发现，第一个非温度的非直集功率为$ t^{6.54} $，它来自fermion biinear biinear biinear biinear biinear biinear biinear biinear birinear $ o_ o_ o_ o_ o_ o_ {1} = us_ {h_ fermion bectial_ {1} $ h_ {1} \大约3.77 $。 $ T^{6.54} $项面前的系数与共形扰动理论的预测非常吻合。我们得出的结论是，即使SYK模型并非严格的保形，同形扰动理论似乎也起作用。
We solve numerically the large $N$ Dyson-Schwinger equations for the Sachdev-Ye-Kitaev (SYK) model utilizing the Legendre polynomial decomposition and reaching $10^{-36}$ accuracy. Using this we compute the energy of the SYK model at low temperatures $T\ll J$ and obtain its series expansion up to $T^{7.54}$. While it was suggested that the expansion contains terms $T^{3.77}$ and $T^{5.68}$, we find that the first non-integer power of temperature is $T^{6.54}$, which comes from the two point function of the fermion bilinear operator $O_{h_{1}}=χ\partial_τ^{3}χ$ with scaling dimension $h_{1}\approx 3.77$. The coefficient in front of $T^{6.54}$ term agrees well with the prediction of the conformal perturbation theory. We conclude that the conformal perturbation theory appears to work even though the SYK model is not strictly conformal.
