  Solids undergoing a transition from order to disorder experience the
proliferation of topological defects. The melting process generates transient
quantum states. However, their dynamical nature with femtosecond lifetime
hinders exploration with atomic precision. Here, we suggest an alternative
approach to the dynamical melting process by focusing on the interface created
by competing degenerate quantum states. We use a scanning tunneling microscope
(STM) to visualize the unidirectional charge density wave (CDW) and its spatial
progression ("static melting") across a twin domain boundary (TDB) in the
layered material GdTe$_{3}$. Combining STM with a spatial lock-in technique, we
reveal that the order parameter amplitude attenuates with the formation of
dislocations and thus two different unidirectional CDWs coexist near the TDB,
reducing the CDW anisotropy. Notably, we discover a correlation between this
anisotropy and the CDW gap. Our study provides valuable insight into the
behavior of topological defects and transient quantum states.
