Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions
In this paper, we propose using the nonlinear sigma model (NLSM) with the Wess-Zumino-Witten (WZW) term as a general description of deconfined quantum critical points that separate two spontaneously symmetry-breaking (SSB) phases in arbitrary dimensions. In particular, we discuss the suitable choice...
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| Format: | Article |
| Language: | English |
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SciPost
2023-07-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.6.3.047 |
| _version_ | 1797785767286669312 |
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| author | Da-Chuan Lu |
| author_facet | Da-Chuan Lu |
| author_sort | Da-Chuan Lu |
| collection | DOAJ |
| description | In this paper, we propose using the nonlinear sigma model (NLSM) with the Wess-Zumino-Witten (WZW) term as a general description of deconfined quantum critical points that separate two spontaneously symmetry-breaking (SSB) phases in arbitrary dimensions. In particular, we discuss the suitable choice of the target space of the NLSM, which is in general the homogeneous space G/K, where $G$ is the UV symmetry and $K$ is generated by ${\mathfrak k}={\mathfrak h}_1\cap {\mathfrak h}_2$, and ${\mathfrak h}_i$ is the Lie algebra of the unbroken symmetry in each SSB phase. With this specific target space, the symmetry defects in both SSB phases are on equal footing, and their intertwinement is captured by the WZW term. The DQCP transition is then tuned by proliferating the symmetry defects. By coupling the $G/K$ NLSM with the WZW term to the background gauge field, the 't Hooft anomaly of this theory can be determined. The bulk symmetry-protected topological (SPT) phase that cancels the anomaly is described by the relative Chern-Simons term in odd spacetime dimensions or mixed $\theta$ term in even dimensions. We construct and discuss a series of models with Grassmannian symmetry defects in 3+1d. We also provide the fermionic model that reproduces the $G/K$ NLSM with the WZW term. |
| first_indexed | 2024-03-13T00:59:38Z |
| format | Article |
| id | doaj.art-f8f0569a6db0466ba78815ed1dccd965 |
| institution | Directory Open Access Journal |
| issn | 2666-9366 |
| language | English |
| last_indexed | 2024-03-13T00:59:38Z |
| publishDate | 2023-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj.art-f8f0569a6db0466ba78815ed1dccd9652023-07-06T13:41:57ZengSciPostSciPost Physics Core2666-93662023-07-016304710.21468/SciPostPhysCore.6.3.047Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensionsDa-Chuan LuIn this paper, we propose using the nonlinear sigma model (NLSM) with the Wess-Zumino-Witten (WZW) term as a general description of deconfined quantum critical points that separate two spontaneously symmetry-breaking (SSB) phases in arbitrary dimensions. In particular, we discuss the suitable choice of the target space of the NLSM, which is in general the homogeneous space G/K, where $G$ is the UV symmetry and $K$ is generated by ${\mathfrak k}={\mathfrak h}_1\cap {\mathfrak h}_2$, and ${\mathfrak h}_i$ is the Lie algebra of the unbroken symmetry in each SSB phase. With this specific target space, the symmetry defects in both SSB phases are on equal footing, and their intertwinement is captured by the WZW term. The DQCP transition is then tuned by proliferating the symmetry defects. By coupling the $G/K$ NLSM with the WZW term to the background gauge field, the 't Hooft anomaly of this theory can be determined. The bulk symmetry-protected topological (SPT) phase that cancels the anomaly is described by the relative Chern-Simons term in odd spacetime dimensions or mixed $\theta$ term in even dimensions. We construct and discuss a series of models with Grassmannian symmetry defects in 3+1d. We also provide the fermionic model that reproduces the $G/K$ NLSM with the WZW term.https://scipost.org/SciPostPhysCore.6.3.047 |
| spellingShingle | Da-Chuan Lu Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions SciPost Physics Core |
| title | Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions |
| title_full | Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions |
| title_fullStr | Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions |
| title_full_unstemmed | Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions |
| title_short | Nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions |
| title_sort | nonlinear sigma model description of deconfined quantum criticality in arbitrary dimensions |
| url | https://scipost.org/SciPostPhysCore.6.3.047 |
| work_keys_str_mv | AT dachuanlu nonlinearsigmamodeldescriptionofdeconfinedquantumcriticalityinarbitrarydimensions |