Matrix product variational formulation for lattice gauge theory

For hamiltonian lattice gauge theory, we introduce the matrix product anzats inspired from density matrix renormalization group. In this method, wavefunction of the target state is assumed to be a product of finite matrices. As a result, the energy becomes a simple function of the matrices, which can be evaluated using a computer. The minimum of the energy function corresponds to the vacuum state. We show that the S=1/2 Heisenberg chain model are well described with the ansatz. The method is also applied to the two-dimensional S=1/2 Heisenberg and U(1) plaquette chain models.