TY - JOUR
T1 - Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model
AU - Dempsey, Ross
AU - Klebanov, Igor R.
AU - Pufu, Silviu S.
AU - Zan, Bernardo
N1 - Publisher Copyright:
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
PY - 2022/10
Y1 - 2022/10
N2 - We 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)10.1103/PhysRevD.13.1043, contains the mass term mlat∑n(-1)nχn†χn, 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 mlat=m-18e2a. 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 θ angle by π. 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.
AB - We 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)10.1103/PhysRevD.13.1043, contains the mass term mlat∑n(-1)nχn†χn, 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 mlat=m-18e2a. 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 θ angle by π. 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.
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U2 - 10.1103/PhysRevResearch.4.043133
DO - 10.1103/PhysRevResearch.4.043133
M3 - Article
AN - SCOPUS:85144617046
SN - 2643-1564
VL - 4
JO - Physical Review Research
JF - Physical Review Research
IS - 4
M1 - 043133
ER -