|
Résumé |
I will talk about a new type of critical quantum liquids, dubbed Stiefel liquids, that can emerge in quantum magnets. Our theory is based on 2+1 dimensional nonlinear sigma models on target space SO(N)/SO(4), supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of 3d CFTs with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well known deconfined quantum critical point and U(1) Dirac spin liquid (i.e. Nf=4 QED3) are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, we conjecture that Stiefel liquids with N>6 are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. I will also discuss a physical way to realize Stiefel liquids (both the Dirac spin liquid and N=7 non-Lagrangian Stiefel liquid) in quantum spin systems, for example, on triangular or kagome lattice, through the intertwinement of symmetry breaking orders. |
