Abstract
We numerically study the single-flavor Schwinger model with a topological -term, which is practically inaccessible by standard lattice Monte Carlo simulations due to the sign problem. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the nontrivial -dependence of several lattice and continuum quantities in the Hamiltonian formulation. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle , thus respecting invariance, while lattice artifacts still depend on . We also confirm that negative masses can be mapped to positive masses by shifting due to the axial anomaly in the continuum, while lattice artifacts nontrivially distort this mapping. This mass regime is particularly interesting for the ()-dimensional QCD analog of the Schwinger model, the sign problem of which requires the development and testing of new numerical techniques beyond the conventional Monte Carlo approach.
3 More- Received 7 August 2019
- Accepted 14 February 2020
DOI:https://doi.org/10.1103/PhysRevD.101.054507
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. Funded by SCOAP3.
Published by the American Physical Society