  The infinite Density Matrix Renormalisation Group (iDMRG) algorithm is a
highly successful numerical algorithm for the study of low-dimensional quantum
systems, and is also frequently used to initialise the more popular finite DMRG
algorithm. Implementations of both finite and infinite DMRG frequently
incorporate support for the protection and exploitation of symmetries of the
Hamiltonian. In common with other variational tensor network algorithms,
convergence of iDMRG to the ground state is not guaranteed, with the risk that
the algorithm may become stuck in a local minimum. In this paper I demonstrate
the existence of a particularly harmful class of physically irrelevant local
minima affecting both iDMRG and to a lesser extent also infinite Time-Evolving
Block Decimation (iTEBD), for which the ground state is compatible with the
protected symmetries of the Hamiltonian but cannot be reached using the
conventional iDMRG or iTEBD algorithms. I describe a modified iDMRG algorithm
which evades these local minima, and which also admits a natural interpretation
on topologically ordered systems with a boundary.
