The contractor renormalization group (CORE) method, a new approach to solving Hamiltonian lattice systems, is introduced. The method combines contraction and variational techniques with the real-space renormalization group approach. It applies to lattice systems of infinite extent and is ideal for studying phase structure and critical phenomena. The CORE approximation is systematically improvable and can treat systems with dynamical fermions. The method is tested using the (1+1)-dimensional Ising model.
The majority-rule, block-spin, renormalization-group transformation for the
d=3 Ising model is studied, with the use of a recently developed technique for calculating renormalized coupling parameters from a single Monte Carlo simulation. Renormalization-group trajectories and the approximate fixed point are calculated. Improvements in the convergence of the Monte Carlo renormalization-group calculations of critical exponents are discussed.
A relatively simple real-space renormalization procedure, due to Ma and Dasgupta and known as Strong-Disorder Renormalization Group (SDRG), provides in principle exact results on the critical properties at the infinite-randomness fixed point of random spin chains. Numerically, SDRG can be efficiently implemented as a renormalization of Matrix Product Operators (MPO-RG). By considering larger blocks than SDRG, MPO-RG was recently used to compute non-critical quantities that are inaccessible to SDRG. In this work, we study the accuracy of the approach and propose two simple and fast improvements. We observe that the accuracy on the ground state energy is improved by a factor at least equal to 4.