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arXiv 0910.5736hep-lat
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格点场论的费米子袋方法

The fermion bag approach to lattice field theories

Shailesh Chandrasekharan

备注：
31 pages, 9 figures, 5 tables
发表信息：
Phys.Rev.D82:025007,2010
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摘要：

我们提出了一种新的方法来解决系统中的费米子符号问题，其中存在一个耦合$U$，使得当它是无限的费米子配对成玻色子，没有费米子置换符号担心。我们认为，作为$U$成为有限的费米子被释放，但自然局限于我们称为{ \em费米子袋}的区域。费米子符号的问题就局限在这些袋子里，可以用行列式技巧来解决。在费米子袋是小的参数制度，其典型的大小不与系统的大小增长，比传统算法更有效的蒙特卡罗方法的建设应该是可能的。在费米子袋随系统尺寸增长的区域，费米子袋方法继续提供解决问题的替代方法，但可能会失去其在效率方面的主要优势。费米子袋方法也为符号问题提供了新的见解和解决方案。一个自然的解决“银焰问题”也出现了。以三维无质量格点Thirring模型为例，介绍了费米子袋方法，并演示了其中的一些特性。我们计算了量子相变的临界指数，并找到了$ν=0.87(2)$和$η=0.62(2)$。

英文摘要：

We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons and there is no fermion permutation sign to worry about. We argue that as $U$ becomes finite fermions are liberated but are naturally confined to regions which we refer to as {\em fermion bags}. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three dimensional massless lattice Thirring model as an example we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find $ν=0.87(2)$ and $η=0.62(2)$.

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