Universality of emergent states in diverse physical systems

Our physics textbooks are dominated by examples of simple weakly-interacting microscopic states, but most of the real world around us is most effectively described in terms of emergent states that have no clear connection to simple textbook states. Emergent states are strongly-correlated and dominated by properties that emerge as a consequence of interactions and are not part of the description of the corresponding weakly-interacting system. This paper proposes a connection of weakly-interacting textbook states and realistic emergent states through fermion dynamical symmetries having fully-microscopic generators of the emergent states. These imply unique truncation of the Hilbert space for the weakly-interacting system to a collective subspace where the emergent states live. Universality arises because the possible symmetries under commutation of generators, which transcend the microscopic structure of the generators, are highly restricted in character and determine the basic structure of the emergent state, with the microscopic structure of the generators influencing emergent state only parametrically. In support of this idea we show explicit evidence that high-temperature superconductors, collective states in heavy atomic nuclei, and graphene quantum Hall states in strong magnetic fields exhibit a near-universal emergent behavior in their microscopically-computed total energy surfaces, even though these systems share essentially nothing in common at the microscopic level and their emergent states are characterized by fundamentally different order parameters.