  We outline a holographic framework that attempts to unify Landau and
beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a
modern understanding of symmetries as topological defects/operators, the
framework uses a topological order to organize the space of quantum systems
with a global symmetry in one lower dimension. The global symmetry naturally
serves as an input for the topological order. In particular, we holographically
construct a String Operator Algebra (SOA) which is the building block of
symmetric quantum systems with a given symmetry $G$ in one lower dimension.
This exposes a vast web of dualities which act on the space of $G$-symmetric
quantum systems. The SOA facilitates the classification of gapped phases as
well as their corresponding order parameters and fundamental excitations, while
dualities help to navigate and predict various corners of phase diagrams and
analytically compute universality classes of phase transitions. A novelty of
the approach is that it treats conventional Landau and unconventional
topological phase transitions on an equal footing, thereby providing a
holographic unification of these seemingly-disparate domains of understanding.
We uncover a new feature of gapped phases and their multi-critical points,
which we dub fusion structure, that encodes information about which phases and
transitions can be dual to each other. Furthermore, we discover that self-dual
systems typically posses emergent non-invertible, i.e., beyond group-like
symmetries. We apply these ideas to $1+1d$ quantum spin chains with finite
Abelian group symmetry, using topologically-ordered systems in $2+1d$. We
predict the phase diagrams of various concrete spin models, and analytically
compute the full conformal spectra of non-trivial quantum phase transitions,
which we then verify numerically.
