非阿贝尔格点场论弱耦合展开的图解Monte-Carlo方法：大N U（N）xU（N）主手征模型
Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
摘要：
我们开发了基于弱耦合展开的非阿贝尔格点场论在t 'Hooft大N极限下的图解蒙特卡罗模拟的数值工具。首先，我们注意到，路径积分措施，这种理论的贡献裸质量项的有效行动，这是成比例的裸耦合常数。这个质量项使微扰膨胀红外有限，并允许直接研究它在大N和无限体积的限制，使用图解蒙特卡罗方法。在D=2维的大N O（N）西格玛模型的精确可解的例子中，我们证明了这种红外有限弱耦合展开除了裸耦合的幂之外，还包含其对数的幂，这让人想起热场论中的重求和微扰理论和没有指数项的复活的反级数。我们用数值方法证明了这些双级数收敛到明显的非微扰动力学质量间隙。在此基础上，我们发展了一种在大N矩阵场论中平面图抽样的Diagrammatic Monte-Carlo算法，并将其应用于D=2的大N U（N）xU（N）非线性西格玛模型（主手征模型）的红外有限弱耦合展开.我们采样到12个领导订单的弱耦合扩展，这是实际的限制设置越来越强的符号问题在高阶。比较传统的蒙特卡罗模拟与图解蒙特卡罗模拟外推到无限N，我们发现一个很好的协议的能量密度，以及为“退禁闭”过渡的临界温度。最后，我们评论的适用性，我们的方法在零和有限密度的平面QCD。
英文摘要：
We develop numerical tools for Diagrammatic Monte-Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First we note that the path integral measure of such theories contributes a bare mass term in the effective action which is proportional to the bare coupling constant. This mass term renders the perturbative expansion infrared-finite and allows to study it directly in the large-N and infinite-volume limits using the Diagrammatic Monte-Carlo approach. On the exactly solvable example of a large-N O(N) sigma model in D=2 dimensions we show that this infrared-finite weak-coupling expansion contains, in addition to powers of bare coupling, also powers of its logarithm, reminiscent of re-summed perturbation theory in thermal field theory and resurgent trans-series without exponential terms. We numerically demonstrate the convergence of these double series to the manifestly non-perturbative dynamical mass gap. We then develop a Diagrammatic Monte-Carlo algorithm for sampling planar diagrams in the large-N matrix field theory, and apply it to study this infrared-finite weak-coupling expansion for large-N U(N)xU(N) nonlinear sigma model (principal chiral model) in D=2. We sample up to 12 leading orders of the weak-coupling expansion, which is the practical limit set by the increasingly strong sign problem at high orders. Comparing Diagrammatic Monte-Carlo with conventional Monte-Carlo simulations extrapolated to infinite N, we find a good agreement for the energy density as well as for the critical temperature of the "deconfinement" transition. Finally, we comment on the applicability of our approach to planar QCD at zero and finite density.
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