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:	Liujun Zou, Yin-Chen He, Chong Wang
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/18dc49ddf42f4ba8b96ab8e07fc5b570
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spelling	oai:doaj.org-article:18dc49ddf42f4ba8b96ab8e07fc5b5702021-12-02T18:00:43ZStiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders10.1103/PhysRevX.11.0310432160-3308https://doaj.org/article/18dc49ddf42f4ba8b96ab8e07fc5b5702021-08-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.031043http://doi.org/10.1103/PhysRevX.11.031043https://doaj.org/toc/2160-3308We 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.Liujun ZouYin-Chen HeChong WangAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 3, p 031043 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Liujun Zou Yin-Chen He Chong Wang Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
description	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.
format	article
author	Liujun Zou Yin-Chen He Chong Wang
author_facet	Liujun Zou Yin-Chen He Chong Wang
author_sort	Liujun Zou
title	Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
title_short	Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
title_full	Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
title_fullStr	Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
title_full_unstemmed	Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
title_sort	stiefel liquids: possible non-lagrangian quantum criticality from intertwined orders
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/18dc49ddf42f4ba8b96ab8e07fc5b570
work_keys_str_mv	AT liujunzou stiefelliquidspossiblenonlagrangianquantumcriticalityfromintertwinedorders AT yinchenhe stiefelliquidspossiblenonlagrangianquantumcriticalityfromintertwinedorders AT chongwang stiefelliquidspossiblenonlagrangianquantumcriticalityfromintertwinedorders
_version_	1718378972622880768

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

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