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Abstract

We propose and study a specific adiabatic path to prepare a family of tensor
network states that are unique ground states of few-body parent Hamiltonians in
finite lattices, which include normal tensor network states, as well as other
relevant non-normal states. This path guarantees a gap and allows for efficient
numerical simulation. In 1D we numerically investigate the preparation of a
family of states with varying correlation lengths and the 1D AKLT state and
show that adiabatic preparation can be much faster than standard methods based
on sequential preparation. We also apply the method to the 2D AKLT state on the
hexagonal lattice for which no method based on sequential preparation is known,
and show that it can be prepared very efficiently for relatively large
lattices.