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

### APA

Wang, C. (2021). Stiefel liquids: possible non-Lagrangian quantum criticality from intertwined orders. Perimeter Institute. https://pirsa.org/21030041

### MLA

Wang, Chong. Stiefel liquids: possible non-Lagrangian quantum criticality from intertwined orders. Perimeter Institute, Mar. 29, 2021, https://pirsa.org/21030041

### BibTex

@misc{ pirsa_PIRSA:21030041, doi = {10.48660/21030041}, url = {https://pirsa.org/21030041}, author = {Wang, Chong}, keywords = {Condensed Matter}, language = {en}, title = {Stiefel liquids: possible non-Lagrangian quantum criticality from intertwined orders}, publisher = {Perimeter Institute}, year = {2021}, month = {mar}, note = {PIRSA:21030041 see, \url{https://pirsa.org}} }

Chong Wang Perimeter Institute for Theoretical Physics

**Talk Type**Scientific Series

**Subject**

## Abstract

We propose a new type of critical quantum liquids, dubbed Stiefel liquids, based on 2+1 dimensional Wess-Zumino-Witten models on target space SO(N)/SO(4). We show that 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, we conjecture that Stiefel liquids with N > 6 are non-Lagrangian, in the sense that the theories do not (at least not easily) admit any weakly-coupled UV completion. Such non-Lagrangian states are beyond the paradigm of parton gauge theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of mean-field construction also makes it 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.