2022/08/22 by Zhengzhi Wu, Linhao Li, Wu, Zhengzhi +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Physics of Superconductivity and Magnetism #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2208.10518
openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nonlinear σ models (NLSM) with topological terms, i.e., Wess-Zumino-Witten (WZW) terms, or topological NLSM, are potent descriptions of many critical points and phases beyond the Landau paradigm. These critical systems include the deconfined quantum critical points (DQCP) between the Neel order and valance bond solid, and the Dirac spin liquid, in which the topological NLSMs are dual descriptions of the corresponding fermionic models or QED theory. In this paper, we propose a dimensional reduction scheme to derive the U(1) gauged topological NLSM in n-dimensional spacetime on a general target space represented by a Hermitian matrix from the dual QED theory. Compared with the famous Abanov-Wiegmann (AW) mechanism, which generally requires the fermions to be Dirac fermions in the infrared (IR), our method is also applicable to non-relativistic fermions in IR, which can have quadratic dispersion or even a Fermi surface. As concrete examples, we construct several two dimensional lattice models, whose IR theories are all the Nf=4 QED3 with fermions of quadratic dispersion and show that its topological NLSM dual description has level-2 WZW terms on the Grassmannian manifold (U(4))/(U(2)× U(2)) coupled with a dynamical U(1) gauge field. We also study 't Hooft anomaly matching and the same effect of defects in both theories, such as interface, gauge monopoles and skyrmions, which further support our duality. Finally, we discuss how the macroscopic symmetries act on the U(1) monopole operators and the corresponding quantum number.