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arXiv:hep-lat/0202014 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Density matrix renormalization group approach to the massive Schwinger model

Tim Byrnes, P. Sriganesh, Robert J. Bursill, Chris J. Hamer

Published Jul 1, 2002• 178 citations
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Abstract

The massive Schwinger model is studied using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of ``half-asymptotic'' particles at a background field $\ensuremath{\theta}=\ensuremath{\pi}$ is confirmed. The predicted phase transition at finite fermion mass $(m/g)$ is accurately located and demonstrated to belong in the 2D Ising universality class.

DOI
10.1103/physrevd.66.013002

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The massive Schwinger model is studied using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of ``half-asymptotic'' particles at a background field \ensuremathθ=\ensuremathπ\ensuremath{\theta}=\ensuremath{\pi}\ensuremathθ=\ensuremathπ is confirmed. The predicted phase transition at finite fermion mass (m/g)(m/g)(m/g) is accurately located and demonstrated to belong in the 2D Ising universality class.
A bstract We use the Grassmann tensor renormalization group method to investigate the N f = 2 Schwinger model with the staggered fermions in the presence of a 2 π periodic θ term in a broad range of mass. The method allows us to deal with the massive staggered fermions straightforwardly and to study the θ dependence of the free energy and topological charge in the thermodynamic limit. Our calculation provides consistent results with not only the analytical solution in the large mass limit but also the previous Monte Carlo studies in the small mass regime. Our numerical results also suggest that the N f = 2 Schwinger model on a lattice has a different phase structure, than the model in the continuum limit.
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