Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model
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 m_{lat}∑_{n}(−1)^{n}χ_{n}^{†}χ_{n}, and setting it to z...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.043133 |
| _version_ | 1797210573806501888 |
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| author | Ross Dempsey Igor R. Klebanov Silviu S. Pufu Bernardo Zan |
| author_facet | Ross Dempsey Igor R. Klebanov Silviu S. Pufu Bernardo Zan |
| author_sort | Ross Dempsey |
| collection | DOAJ |
| description | 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 m_{lat}∑_{n}(−1)^{n}χ_{n}^{†}χ_{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−1/8e^{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 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. |
| first_indexed | 2024-04-24T10:12:45Z |
| format | Article |
| id | doaj.art-55f0fe123e98428e9f0bea5fafe53880 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:12:45Z |
| publishDate | 2022-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-55f0fe123e98428e9f0bea5fafe538802024-04-12T17:26:32ZengAmerican Physical SocietyPhysical Review Research2643-15642022-11-014404313310.1103/PhysRevResearch.4.043133Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger modelRoss DempseyIgor R. KlebanovSilviu S. PufuBernardo ZanWe 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 m_{lat}∑_{n}(−1)^{n}χ_{n}^{†}χ_{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−1/8e^{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 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.http://doi.org/10.1103/PhysRevResearch.4.043133 |
| spellingShingle | Ross Dempsey Igor R. Klebanov Silviu S. Pufu Bernardo Zan Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model Physical Review Research |
| title | Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model |
| title_full | Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model |
| title_fullStr | Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model |
| title_full_unstemmed | Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model |
| title_short | Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model |
| title_sort | discrete chiral symmetry and mass shift in the lattice hamiltonian approach to the schwinger model |
| url | http://doi.org/10.1103/PhysRevResearch.4.043133 |
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