## Anomalies and Renormalization of Impure States in Quantum Theories    [PDF]

Kumar S. Gupta, Amilcar Queiroz
In a Hamiltonian approach to anomalies parity and time reversal symmetries can be restored by introducing suitable impure 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 framework, leading to a set of $\beta$-functions in the moduli space of the operators. 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 scenario may be relevant for long wavelength descriptions of condensed matter systems such as the quantum spin Hall effect.
View original: http://arxiv.org/abs/1306.5570