Critical behavior of the two-dimensional Ising model in a transverse field: A density-matrix renormalization calculation

We have adjusted the density-matrix renormalization method to handle two-dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we can force certain symmetry properties to the resulting ground-state wave function. Combining the results obtained for system sizes up to $30\times 6$ and finite-size scaling, we derive the phase-transition point and the critical exponent for the gap in the Ising model in a transverse field on a two-dimensional square lattice.