2013/06/30 by Kumar S. Gupta, Amilcar de Queiroz, Amilcar Queiroz
Mathematics · Physics and Astronomy · #Hamiltonian (control theory) #Homogeneous space #Mass gap #Observable #Parity (physics) #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Renormalization #Renormalization group #Topological Materials and Phenomena #cond-mat.str-el #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1142/s0217732314500643
5 pages; v2: small changes in abstract, main text was improved, reference added
arxiv created 2013/07/03 · openalex publication_date 2014/04/17 · arxiv updated 2015/06/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In a Hamiltonian approach to anomalies, parity and time-reversal symmetries can be restored by introducing suitable impure (or mixed) states. However, the expectation values of observables such as the Hamiltonian diverges in such impure states. Here, we show that such divergent expectation values can be treated within a renormalization group (RG) framework, leading to a set of β-functions in the moduli space of the operators representing the observables. This leads to well-defined expectation values of the Hamiltonian in a phase where the impure state restores the P and T symmetry. We also show that this RG procedure leads to a mass gap in the spectrum. Such a framework may be relevant for long wavelength descriptions of condensed matter systems such as the quantum spin Hall (QSH) effect.