  Isotope shifts of transition frequencies in atoms constrain generic long- and
intermediate-range interactions. We focus on new physics scenarios that can be
most strongly constrained by King Linearity Violation such as models with B-L
vector bosons, Higgs portal and chameleon. With the anticipated precision, King
Linearity Violation has the potential to set the strongest laboratory bounds on
these models in some regions of parameter space. Furthermore, we show that this
method can probe the couplings relevant for the protophobic interpretation of
the recently reported Be anomaly. We extend the formalism to include an
arbitrary number of transitions and isotope pairs and fit the new physics
coupling to the currently available isotope shift measurements.
