解决一个古老的故事：Thirring模型在顶针正则化中的解
Settling an old story: solution of the Thirring model in thimble regularization
摘要：
格点场论的顶针正则化已被提出作为臭名昭著的符号问题的解决方案。它在概念上非常简洁和强大，但在实践中受到一个潜在的非常严重的问题的限制：一般来说，许多顶针可以有助于函数积分的计算。半古典主义的论点认为，基本顶针可能足以得到正确的答案，但这一假设已被证明不成立。这种失败的第一个例子已经在Thirring模型的上下文中提出：主导顶针近似仅在理论的参数空间的给定区域中有效。从那时起，这个（简单的）模型在顶针正则化中的完整解决方案一直缺失。在本文中，我们表明，一个完整的解决方案（采取连续极限）确实是可能的。这是可能的，这要归功于我们最近提出的一种方法，这种方法实际上避免了在许多顶针上进行模拟的需要。
英文摘要：
Thimble regularisation of lattice field theories has been proposed as a solution to the infamous sign problem. It is conceptually very clean and powerful, but it is in practice limited by a potentially very serious issue: in general many thimbles can contribute to the computation of the functional integrals. Semiclassical arguments would suggest that the fundamental thimble could be sufficient to get the correct answer, but this hypothesis has been proven not to hold true in general. A first example of this failure has been put forward in the context of the Thirring model: the dominant thimble approximation is valid only in given regions of the parameter space of the theory. Since then a complete solution of this (simple) model in thimble regularisation has been missing. In this paper we show that a full solution (taking the continuum limit) is indeed possible. It is possible thanks to a method we recently proposed which de facto evades the need to simulate on many thimbles.
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