Gauge invariance in a Z_2 hamiltonian lattice gauge theory

Abstract

We propose an efficient variational method for $Z_2$ lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.Comment: 6 pages, 2 figures. Talk presented at Lattice2005 (Non-zero temperature and density), 25-30 July 2005, Trinity College, Dublin, Irelan