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arXiv:2001.07373 · Physical review. B./Physical review. B

Global anomaly matching in the higher-dimensional CPN−1 model

Takuya Furusawa, Masaru Hongo

Published Apr 13, 2020• 8 citations
arXivHTMLPDF

Abstract

We investigate 't Hooft anomalies in the ${\mathbb{C}\mathbb{P}}^{N\ensuremath{-}1}$ model in space-time dimensions higher than two and identify two types of anomalies: one is a mixed anomaly between the $\mathrm{PSU}(N)$ flavor-rotation and magnetic symmetries and the other is between the reflection and magnetic symmetries. The latter indicates that even in the absence of the flavor symmetry, the model cannot have a unique gapped ground state as long as the reflection and magnetic symmetries are respected. We also clarified the condition for the 't Hooft anomalies to survive under monopole deformations, which explicitly break the magnetic symmetry down to its discrete subgroup. Besides, we explicitly show how the identified 't Hooft anomalies match in the low-energy effective description of symmetry broken phases---the N\'eel, $\mathrm{U}(1)$ spin liquid, and the valence bond solid phases. An application to the finite-temperature phase diagram of the four-dimensional ${\mathbb{C}\mathbb{P}}^{N\ensuremath{-}1}$ model is also discussed.

DOI
10.1103/physrevb.101.155113

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CCC-PPP-TTT anomaly in bosonic systems
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't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by ∼a1∧a2∧a3∧a4\sim a_1\wedge a_2\wedge a_3\wedge a_4∼a1​∧a2​∧a3​∧a4​, where the aia_iai​ denote background gauge fields for the global symmetries. Through explicit lattice gauging, we demonstrate the emergence of higher symmetry structures, including 2-group, non-invertible, and higher fusion categorical symmetries. We also provide a field-theoretical understanding of these results. Applying this framework to systems with Lieb-Schultz-Mattis anomalies, obtained by promoting part of the internal symmetries to translational symmetries, we demonstrate that modulated (dipole) symmetries arise as direct counterparts of those in systems with purely internal typeIV anomalies. Importantly, we uncover a qualitatively new feature absent in previously studied modulated symmetries: their realization can become intrinsically defect-dependent. In particular, the emergent symmetry structure changes depending on whether symmetry defects are present. This work establishes a concrete lattice realization of mixed anomalies and reveals a rich structure of emergent symmetries, thereby clarifying their role in constraining quantum phases of matter.