Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
We propose a new type of quantum liquids, dubbed Stiefel liquids, 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 critical quantum liquids with extraordinary properties, such...
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| Autores principales: | , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
American Physical Society
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/18dc49ddf42f4ba8b96ab8e07fc5b570 |
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| Sumario: | We propose a new type of quantum liquids, dubbed Stiefel liquids, 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 critical quantum liquids 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 are unified as two special examples of Stiefel liquids, 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. 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 (conventional or partonlike) mean-field construction also means that, within the traditional approaches, will be difficult to decide whether a non-Lagrangian state can actually 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 noncoplanar magnetic orders and valence-bond-solid orders. |
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