Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential ${\mu }_B$ is a well-known method to bypass the sign problem of lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients, various alternative expansion schemes as well as resummation techniques have been suggested to extend the Taylor series to larger values of ${\mu }_B$. Recently, a way to resum the contribution of the first $N$ charge density correlation functions $D_1,\dots ,D_N$ to the Taylor series to all orders in ${\mu }_B$ was proposed in [Phys. Rev. Lett. 128, 022001 (2022)]. The resummation takes the form of an exponential factor. Since the correlation functions are calculated stochastically, the exponential factor contains a bias which can be significant for large $N$ and ${\mu }_B$. In this paper, we present a new method to calculate the QCD equation of state based on the well-known cumulant expansion from statistics. By truncating the expansion at a maximum order $M$, we end up with only finite products of the correlation functions which can be evaluated in an unbiased manner. Although our formalism is also applicable for ${\mu }_B\ne 0$, here we present it for the simpler case of a finite isospin chemical potential ${\mu }_I$ for which there is no sign problem. We present and compare results for the pressure and the isospin density obtained using Taylor expansion, exponential resummation and cumulant expansion, and provide evidence that the absence of bias in the latter actually improves the convergence.

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在有限化学势下恢复晶格 QCD 泰勒级数状态方程的新方法

（重）化学势幂的热力学势的泰勒展开${\mu }_{乙}$是一种众所周知的绕过点阵 QCD 符号问题的方法。由于计算高阶泰勒系数的困难，已经提出了各种替代展开方案以及求和技术来将泰勒级数扩展到更大的值${\mu }_{乙}$. 最近，一个恢复第一个贡献的方法$ñ$电荷密度相关函数$D_1,\dots ,D_{ñ}$到泰勒级数到所有订单${\mu }_{乙}$在[物理学]中提出。牧师莱特。 128 , 022001 (2022)]。恢复采用指数因子的形式。由于相关函数是随机计算的，因此指数因子包含一个偏差，对于较大的$ñ$和${\mu }_{乙}$. 在本文中，我们提出了一种基于统计学中众所周知的累积量展开计算 QCD 状态方程的新方法。通过以最大顺序截断扩展$米$，我们最终只能得到相关函数的有限乘积，这些乘积可以以无偏的方式进行评估。虽然我们的形式主义也适用于${\mu }_{乙}\ne 0$，这里我们将其用于有限同位旋化学势的更简单情况${\mu }_{我}$没有符号问题。我们展示并比较了使用泰勒展开、指数重和和累积展开获得的压力和同位旋密度的结果，并提供证据表明后者中没有偏差实际上提高了收敛性。