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Pure gauge theories are rather different from theories with pure scalar andfermionic matter, especially in terms of the nature of excitations. Forexample, in scalar and fermionic theories, one can create ultra-localexcitations. For a gauge theory, such excitations need to be closed loops thatdo not violate gauge invariance. In this proceedings, we present a study on thecondensation phenomenon associated with the string-like excitations of anAbelian lattice gauge theory. These phenomena are studied through numericalsimulations of a $U(1)$ quantum link model in 2+1 dimensions in a laddergeometry using matrix product states. In this proceedings, we show theexistence of ground states characterized by the presence of such string-likeexcitations. These are caused due to the condensation of torelons. We alsostudy the relationship between the properties of the plaquettes in the groundstate and the presence of such condensation phenomenon.

Phases at finite winding number of an Abelian lattice gauge theory