  The numerical study of anyonic systems is known to be highly challenging due
to their non-bosonic, non-fermionic particle exchange statistics, and with the
exception of certain models for which analytical solutions exist, very little
is known about their collective behaviour as a result. Meanwhile, the density
matrix renormalisation group (DMRG) algorithm is an exceptionally powerful
numerical technique for calculating the ground state of a low-dimensional
lattice Hamiltonian, and has been applied to the study of bosonic, fermionic,
and group-symmetric systems. The recent development of a tensor network
formulation for anyonic systems opened up the possibility of studying these
systems using algorithms such as DMRG, though this has proved challenging both
in terms of programming complexity and computational cost. This paper presents
the implementation of DMRG for finite anyonic systems, including a detailed
scheme for the implementation of anyonic tensors with optimal scaling of
computational cost. The anyonic DMRG algorithm is demonstrated by calculating
the ground state energy of the Golden Chain, which has become the benchmark
system for the numerical study of anyons, and is shown to produce results
comparable to those of the anyonic TEBD algorithm and superior to the
variationally optimised anyonic MERA, at far lesser computational cost.
