11 pages, 1 figure, discussion of renormalization of four-momentum modified, increased numerical precision of one-loop integrals, results and conclusions unchanged
Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which contains a linearly divergent piece. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the latter are equal to one.
We use the two-dimensional Schwinger model to investigate how lattice fermions perceive the global topological charge $q\in\mathbf{Z}$ of a given gauge background $U$. After a warm-up part devoted to staggered, Adams, Wilson and naive fermions, we consider Karsten-Wilczek and Borici-Creutz fermions, which are in the class of minimally doubled lattice fermion actions. We focus on the eigenvalue spectrum and the chiralities of the pertinent eigenmodes. Without modification both minimally doubled actions are found to be insensitive to topology, but in either case it is possible to define a suitab…
The two-dimensional Schwinger model is used to explore how lattice fermion operators perceive the global topological charge $q \in \mathbb{Z}$ of a given background gauge field. We focus on Karsten-Wilczek and Borici-Creutz fermions, which are minimally doubled, and compare them to Wilson, Brillouin, naive, staggered and Adams fermions. For each operator the eigenvalue spectrum in a background with $q \neq 0$ is determined along with the chiralities of the eigenmodes, and the spectral flow of the pertinent hermitean operator is worked out. We find that Karsten-Wilczek and Borici-Creutz fermion…
Topological Minimally Entangled States via Geometric Measure
在这里，我们展示了如何最小纠缠态（MES）的二维系统的拓扑顺序可以识别使用的纠缠的几何措施。我们表明这一点，通过最大限度地减少这一措施的双重半，双斐波那契和环面代码模型上的环面与非平凡的拓扑分区。我们的计算要么是对小系统尺寸的准精确计算，要么是使用[R]中的张量网络方法。Orus，T. C. Wei，O. Buerschaper，A. Garcia-Saez，arXiv：1406.0585]用于大尺寸。作为我们方法的副产品，我们看到几何纠缠的最小化也可以确定给定模型中阿贝尔准粒子激发的数量。本文的结果为从二维量子晶格模型的基态多体纠缠结构中提取其完整的拓扑信息提供了一种非常有效和精确的方法。
We focus on the four-dimensional central-branch Wilson fermion, which makes good use of six species at the central branch of the Wilson Dirac spectrum and possesses the extra $U(1)_{\overline V}$ symmetry. With introducing new insights we discuss the prohibition of additive mass renormalization for all the six species, SSB of $U(1)_{\overline V}$ in strong-coupling QCD, the absence of the sign problem, and the usefulness for many-flavor QCD simulation. We then construct several varieties of the central-branch fermions and study their properties. In particular, we investigate the two-flavor ver…
