  We show how the tracer motion of tagged, distinguishable particles can
effectively describe transport in various homogeneous quantum many-body systems
with constraints. We consider systems of spinful particles on a one-dimensional
lattice subjected to constrained spin interactions, such that some or even all
multipole moments of the effective spin pattern formed by the particles are
conserved. On the one hand, when all moments - and thus the entire spin pattern
- are conserved, dynamical spin correlations reduce to tracer motion
identically, generically yielding a subdiffusive dynamical exponent $z=4$. This
provides a common framework to understand the dynamics of several constrained
lattice models, including models with XNOR or $tJ_z$ - constraints. We consider
random unitary circuit dynamics with such a conserved spin pattern and use the
tracer picture to obtain exact expressions for their late-time dynamical
correlations. Our results can also be extended to integrable quantum many-body
systems that feature a conserved spin pattern but whose dynamics is insensitive
to the pattern, which includes for example the folded XXZ spin chain. On the
other hand, when only a finite number of moments of the pattern are conserved,
the dynamics is described by a convolution of the internal hydrodynamics of the
spin pattern with a tracer distribution function. As a consequence, we find
that the tracer universality is robust in generic systems if at least the
quadrupole moment of the pattern remains conserved. In cases where only total
magnetization and dipole moment of the pattern are constant, we uncover an
intriguing coexistence of two processes with equal dynamical exponent but
different scaling functions, which we relate to phase coexistence at a first
order transition.
