Special Discrete Symmetries

Walter Greiner, Berndt Müller

William Martin McClain

Jochen Endrejat, H. Büttner

Within a special multi-coin quantum walk scheme, we analyse the effect of the entanglement of the initial coin state. For states with a special entanglement structure, it is shown that this entanglement can be measured with the mean value of the walk, which depends on the i-concurrence of the initial coin state. Further, the entanglement evolution is investigated and it is shown that the symmetry of the probability distribution is reflected by the symmetry of the entanglement distribution.

Daniel Braak

The quantum Rabi model is the simplest and most important theoretical description of light–matter interaction for all experimentally accessible coupling regimes. It can be solved exactly and is even integrable due to a discrete symmetry, the Z 2 or parity symmetry. All qualitative properties of its spectrum, especially the differences to the Jaynes–Cummings model, which possesses a larger, continuous symmetry, can be understood in terms of the so-called “G-functions” whose zeroes yield the exact eigenvalues of the Rabi Hamiltonian. The special type of integrability appearing in systems with discrete degrees of freedom is responsible for the absence of Poissonian level statistics in the spectrum while its well-known “Juddian” solutions are a natural consequence of the structure of the G-functions. The poles of these functions are known in closed form, which allows drawing conclusions about the global spectrum.

Kurt Gottfried, Tung‐Mow Yan

Pramod Padmanabhan, Somnath Maity, Akash Sinha +1 more

The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation. When spectral parameters are included, such equations are expected to lead to integrable Hamiltonians with local interactions involving multiple degrees of freedom. In this work we characterize both the continuous and discrete symmetries of these equations required to establish an equivalence class of solutions. We find that the set of such symmetries depends on the number of sites on which the equation is supported. In several cases there are more symmetries than the standard Yang-Baxter equation, thus placing heavy constraints on the number of inequivalent solutions and the associated integrable models. As an application we show how to restrict the generic $16\times16$ ansatz to the 30-dimensional subspace invariant under a chosen discrete symmetry subgroup. An explicit $16\times 16$ solution is also written down. 21 pages + References ; v2 31 pages, Includes several new symmetries, with an exhaustive account of permutation symmetries, and a new section on application of these methods, Published in "A Special Issue in Honour of Jarmo Hietarinta''