Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model
Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model
复制标题
DOI：
10.1103/physrevresearch.4.043133
复制
发表时间：
2022-11-28
影响因子：
4.2
通讯作者：
Zan, Bernardo
中科院分区：
文献类型：
--
作者：
Dempsey, Ross;Klebanov, Igor R.;Zan, Bernardo
使用交错费米子的Kogut-Susskind哈密顿方法重新审视Schwinger模型的晶格公式。由Banks等人在Phys.Rev.D13，1043（1976）中介绍的这个模型包含质量项mlat Sigma n（-1）（n）x（n）（+）x（n），并且通常假定将其设置为零以提供无质量Schwinger模型的晶格正则化。相反，我们认为晶格和连续介质质量参数之间的关系应取为m（lat）= m - 1/ 8 e（2）a。m = 0的模型具有离散的手征对称性，这是由单位晶格平移伴随着由π的θ角的移位产生的。虽然随着晶格间距a接近零，质量位移消失，但我们发现，包括这种位移大大提高了收敛到连续极限的速度。我们证明了更快的收敛速度，使用数值对角化的有限晶格系统，以及外推的晶格强耦合扩展。
revisit the lattice formulation of the Schwinger model using the Kogut-Susskind Hamiltonian approach with staggered fermions. This model, introduced by Banks et al. Phys. Rev. D 13, 1043 (1976), contains the mass term mlat Sigma n (-1)(n)x(n)(+) x(n), and setting it to zero is often assumed to provide the lattice regularization of the massless Schwinger model. We instead argue that the relation between the lattice and continuum mass parameters should be taken as m(lat) = m - 1/ 8 e(2)a. The model with m = 0 is shown to possess a discrete chiral symmetry that is generated by the unit lattice translation accompanied by the shift of the theta angle by pi. While the mass shift vanishes as the lattice spacing a approaches zero, we find that including this shift greatly improves the rate of convergence to the continuum limit. We demonstrate the faster convergence using both numerical diagonalizations of finite lattice systems, as well as extrapolations of the lattice strong coupling expansions.