Kadanoff Seminar - Stiefel liquids: possible non-Lagrangian quantum criticality from intertwined orders - Linjun Zou, Perimeter Institute

1:30 pm VIA ZOOM

Stiefel liquids: possible non-Lagrangian quantum criticality from intertwined orders.

I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders.

Event Type


Oct 25