论文标题
2+1 $ d $ thirring型号的光谱与$ n = 1 $ domain wall fermions
Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions
论文作者
论文摘要
我们在2+1+1尺寸的晶格上采用了域壁费（DWF）公式，并执行$ n = 1 $ floation Monte Carlo模拟。在关键的交互强度下，模型具有自发的$ \ mathrm {u}（2）\ rightarrow \ Mathrm {u}（1）\ otimes \ otimes \ Mathrm {u}（1）$ symmetry breaking;我们在两个阶段中分析了戈金石和非金石的诱导的旋转0介子，以及福尔米金准粒子的相关因子。至关重要的是，我们在关键点确定了异常的尺寸$η_ψ\约3 $，与3 $ d $中的总纽扣模型形成鲜明对比，并与交错的费米子获得了结果。我们的数值模拟通过对自由费米昂相关器的分析处理进行了补充，该方法由于福尔米恩（Fermion）与其较重的倍增器的未结合相互作用而引起的传播器中的分支切割，表现出大量的早期伪像。这些伪像是可以推广的，除了扭转模型之外，是DWF的固有特性，或更一般的Ginsparg-Wilson费米子。
We employ the domain wall fermion (DWF) formulation of the Thirring model on a lattice in 2+1+1 dimensions and perform $N=1$ flavor Monte Carlo simulations. At a critical interaction strength the model features a spontaneous $\mathrm{U}(2)\rightarrow\mathrm{U}(1)\otimes \mathrm{U}(1)$ symmetry breaking; we analyse the induced spin-0 mesons, both Goldstone and non-Goldstone, as well as the correlator of the fermion quasiparticles, in both resulting phases. Crucially, we determine the anomalous dimension $η_ψ\approx 3$ at the critical point, in stark contrast with the Gross-Neveu model in 3$d$ and with results obtained with staggered fermions. Our numerical simulations are complemented by an analytical treatment of the free fermion correlator, which exhibits large early-time artifacts due to branch cuts in the propagator stemming from unbound interactions of the fermion with its heavy doublers. These artifacts are generalisable beyond the Thirring model, being an intrinsic property of DWF, or more generally Ginsparg-Wilson fermions.
