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arXiv:hep-lat/0201007 · Nuclear Physics B - Proceedings Supplements

Density matrix renormalisation group approach to the massive Schwinger model

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

Published May 1, 2002• 38 citations
arXivHTMLPDF
DOI
10.1016/s0920-5632(02)01416-0

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Density matrix renormalization group approach to the massive Schwinger model

Tim Byrnes, P. Sriganesh, Robert J. Bursill +1 more

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.

arXiv:hep-lat/0202014•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 1, 2002•178 citations
Numerical investigations of the XY model, the Heisenberg model and the J-J' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels are obtained and finite size scaling is performed to estimate the bulk limit values. The results are found to be consistent with the exact values. The DMRG results are found to be most promising. The Schwinger model is also studied using the exact diagonalisation and the strong coupling expansion. The massless, the massive model and the model with a background electric field are explored. Ground state energy, scalar and vector particle masses and order parameters are examined. The achieved values are observed to be consistent with previous results and theoretical predictions. Path to the future studies is outlined.
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)(m/g)(m/g) is accurately located and demonstrated to belong in the 2D Ising universality class.