Minimally doubled chiral fermions with C, P and T symmetry on the staggered lattice
Jutho Haegeman, Henri Verschelde
备注：
Withdrawn due to the fact that the proposed approach is restricted to discrete chiral symmetry and not easily generalizable to continuous chiral symmetry
Recently, the interest in local lattice actions for chiral fermions has revived, with the proposition of new local actions in which only the minimal number of doublers appear. The trigger role of graphene having a minimally doubled, chirally invariant, Dirac-like excitation spectrum can not be neglected. The challenge is to construct an action which preserves enough symmetries to be useful in lattice gauge calculations. We present a new approach to obtain local lattice actions for fermions using a reinterpretation of the staggered lattice approach of Kogut and Susskind. This interpretation is based on the similarity with the staggered lattice approach in FDTD simulations of acoustics and electromagnetism. It allows us to construct a local action for chiral fermions which has all discrete symmetries and the minimal number of fermion flavors, but which is non-Hermitian in real space. However, we argue that this will not pose a threat to the usability of the theory.
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…
I discuss minimally doubled fermions fermions as an ultra-local formulation on the lattice for sea quarks that realize a non-singlet chiral symmetry. I introduce a non-singlet mass term for Karsten-Wilczek fermions and identify the appropriate representation of the SU(2) flavor group at finite lattice spacing. I present an algebraic proof that the symmetry of the quark determinant under charge conjugation and reflections of the Euclidean axes is preserved for Karsten-Wilczek fermions as sea quarks. Finally, I discuss how the flavor components in meson correlation functions with Karsten-Wilczek…
Most quark actions in lattice QCD encounter difficulties with chiral symmetry and its spontaneous breakdown. Minimally doubled fermions (MDF) are a category of strictly local chiral lattice fermions, whose continuum limit reproduces two degenerate quark flavours. The two poles of their Dirac operator are aligned such that symmetries under charge conjugation or reflection of one particular direction are explictly broken at finite lattice spacing. Properties of MDF are scrutinised with regard to broken symmetry and meson spectrum to discern their suitability for numerical studies of QCD. Interac…
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。
Minimally doubled fermion proposed by Creutz and Borici is a promising chiral fermion formulation on lattice. In this work, we present excited state mass spectroscopy for the meson bound states in Gross-Neveu model using Borici-Creutz fermion. We also evaluate the effective fermion mass as a function of coupling constant which shows a chiral phase transition at strong coupling. The lowest lying meson in 2-dimensional QED is also obtained using Borici-Creutz fermion.
Minimally doubled fermion proposed by Creutz and Borici is a promising chiral fermion formulation on lattice. In this work, we present excited state mass spectroscopy for the meson bound states in Gross-Neveu model using Borici-Creutz fermion. We also evaluate the effective fermion mass as a function of coupling constant which shows a chiral phase transition at strong coupling. The lowest lying meson in 2-dimensional QED is also obtained using Borici-Creutz fermion.
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…
