Exact ground state, mass gap, and string tension in lattice gauge theory

We make use of the arbitrariness in defining lattice gauge theory to propose a new form of lattice Hamiltonian with exact ground state. Four such Hamiltonians are obtained. Since the ground state is exactly known, a variational method is applied to obtain rigorous upper bounds of the mass gap in (2+1)-dimensional U(1), SU(2), and SU(3) lattice gauge theories. Trial wave functions for excited states contain loop variables up to 30×30 Wilson loops. Nice scaling behaviors are obtained. The scaling behaviors of the mass gap and string tension in non-Abelian theory are in agreement with that predicted by weak-coupling perturbation theory and the Monte Carlo method, but is extended to a much weaker coupling region 1/$g^2$∼7. For non-Abelian theory, universality is confirmed.