One of the central themes of quantum many-body physics and quantum field theory is the emergence of universality classes at large scales out of the microscopic constitutes at small scales. However, it is often rather difficult to identify in a controlled manner the universality class based on the microscopic physics of the system. I will discuss the inverse problem of the previous one, i.e. the “emergibility problem”: given a universality class, from which microscopic systems can it emerge? I will argue that quantum anomaly provides powerful insight into the emergibility problem, based on which I will establish a framework for it. I will present the results obtained by applying this framework to study the emergibility of a family of exotic universality classes, dubbed “Stiefel liquids”. The Stiefel liquids form an infinite family that unify the celebrated deconfined quantum critical point and Dirac spin liquid and generalize them to possibly non-Lagrangian quantum critical states. Our anomaly-based framework for the emergibility problem allows us to predict all different realizations and specific properties of the Stiefel liquids in various frustrated magnets, such as triangular lattice spin-1/2 systems. Most of the realizations we identify were not envisioned before, and some of them cannot be described using the conventional approach.

Refs:
Ye, Guo, He, Wang, Zou, arXiv: 2111.12097.
Zou, He, Wang, arXiv: 2101.07805.

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