Real space renormalisation group for a fermion system: An improved scheme

A new scheme has been developed to find the renormalisation prescription in an existing real space quantum renormalisation group technique suitable for studying the ground states of many fermion systems. The method is applied here to a non-interacting many fermion system for illustration and comparison with the exact solution. It turns out that this method generates a very good upper bound to the ground state energy and its convergence to the exact result is much more efficient than in the existing renormalisation prescriptions. The method seems to be a promising tool for probing the ground states of low dimensional correlated fermion systems.