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We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance is that of {em holographic symmetry}. It reflects situations wherein global symmetries become, under a duality mapping, symmetries that act solely on the systems boundary. Holographic symmetries are naturally related to edge modes and localization. The utility of our approach is illustrated by systematically deriving generalized order parameters for pure and matter-coupled Abelian gauge theories, and for some models of topological matter.
We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using topological qu
Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one generic approach we develop form factor expansions, for ground states and generalized Gibbs ensembles (GGE), and compare the so obtained results with predictions fro
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully-frustrated XY m
We discuss the higher-order topological field theory and response of topological crystalline insulators with no other symmetries. We show how the topology and geometry of the system is organised in terms of the elasticity tetrads which are ground sta
We study the Killing vectors of the quantum ground-state manifold of a parameter-dependent Hamiltonian. We find that the manifold may have symmetries that are not visible at the level of the Hamiltonian and that different quantum phases of matter exh