  Pure gauge theories are rather different from theories with pure scalar and
fermionic matter, especially in terms of the nature of excitations. For
example, in scalar and fermionic theories, one can create ultra-local
excitations. For a gauge theory, such excitations need to be closed loops that
do not violate gauge invariance. In this proceedings, we present a study on the
condensation phenomenon associated with the string-like excitations of an
Abelian lattice gauge theory. These phenomena are studied through numerical
simulations of a $U(1)$ quantum link model in 2+1 dimensions in a ladder
geometry using matrix product states. In this proceedings, we show the
existence of ground states characterized by the presence of such string-like
excitations. These are caused due to the condensation of torelons. We also
study the relationship between the properties of the plaquettes in the ground
state and the presence of such condensation phenomenon.
