Multiple symmetries

You-Fei Xie, Qing‐Hu Chen

Abstract The true level crossing in the asymmetric quantum Rabi model without any obvious symmetry can be exhibited in the energy spectrum if the qubit bias is a multiple of the cavity frequency, which should imply the existence of the hidden symmetry. In this work, within a Bogoliubov operator approach, we can readily derive the symmetry operators associated with the hidden symmetry hierarchically for arbitrary multiples. The symmetry operators for small multiples in the literature can be extremely easily reproduced in our general scheme. In addition, a general parity operator is defined through the symmetry operator, which naturally includes the well-known parity operator of the symmetric model. We believe that the present approach can be straightforwardly extended to other asymmetric Rabi models to find the relevant symmetry operators.

Stefan Flörchinger

Kurt Gottfried, Tung‐Mow Yan

N. A. Slavnov

We consider quantum integrable models with the gl(2|1) symmetry and derive a set of multiple commutation relations between the monodromy matrix elements. These multiple commutation relations allow obtaining different representations for Bethe vectors.

Roland Cristopher F. Caballar, Leonard R. Ocampo, Eric A. Galapon

Internal symmetries can be used to classify multiple solutions to the time-energy canonical commutation relation (TE-CCR). The dynamical behavior of solutions to the TE-CCR possessing particular internal symmetries involving time reversal differ significantly from solutions to the TE-CCR without those particular symmetries, implying a connection between the internal symmetries of a quantum system, its internal unitary dynamics, and the TE-CCR.

K. Tamvakis