Universality and mass gaps for a series of lattice Hamiltonians with exact ground states

Abstract

A series of lattice Hamiltonians with exact ground states and the same correct continuum limit are obtained by using the arbitrariness in defining lattice gauge theories. The rigorous upper bounds of the mass gaps in (2+1)-dimensional SU(2) theory are obtained by the variational method. Trial wave functions for excited states contain loop variables up to 130\ifmmode\times\else\texttimes\fi{}130 Wilson loops, whose coefficients we take as variational parameters. The results show the same scaling behavior am=2.27${g}^{2}$ extended to a very deep weak-coupling region (1/${g}^{2}$\ensuremath{\sim}7) and confirm the universality in lattice gauge theory.