TY  - JOUR
AU  - Leiner, David
AU  - Zeier, Robert
AU  - Glaser, Steffen J.
TI  - Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
JO  - Journal of physics / A Mathematical and theoretical
VL  - 53
IS  - 49
SN  - 0022-3689
CY  - Bristol
PB  - IOP Publ.
M1  - FZJ-2020-02018
SP  - 495301
PY  - 2020
AB  - We study the representation and visualization of finite-dimensional, coupled quantum systems. To establish a generalized Wigner representation, multi-spin operators are decomposed into a symmetry-adapted tensor basis and are mapped to multiple spherical plots that are each assembled from linear combinations of spherical harmonics. We explicitly determine the corresponding symmetry-adapted tensor basis for up to six coupled spins 1/2 (qubits) using a first step that relies on a Clebsch-Gordan decomposition and a second step which is implemented with two different approaches based on explicit projection operators and coefficients of fractional parentage. The approach based on explicit projection operator is currently only applicable for up to four spins 1/2. The resulting generalized Wigner representation is illustrated with various examples for the cases of four to six coupled spins 1/2. We also treat the case of two coupled spins with arbitrary spin numbers (qudits) not necessarily equal to 1/2 and highlight a quantum system of a spin 1/2 coupled to a spin 1 (qutrit). Our work offers a much more detailed understanding of the symmetries appearing in coupled quantum systems.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000615524500001
DO  - DOI:10.1088/1751-8121/ab93ff
UR  - https://juser.fz-juelich.de/record/875409
ER  -