Investigation of the Aharonov-Bohm and Aharonov-Casher topological phases for quantum entangled states

Highlights: • The Aharonov-Bohm and Aharonov-Casher effects are examined with a full relativistic treatment in Hamiltonian formalism. • The framework is applied for quantum entangled spin states and the related quantum correlations are investigated. • AB type topological effects are compared, similarities and differences are presented in a table. Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects are treated fully relativistically in 2+1 dimensions. The influences of the relevant geometric and topological phases on an entangled spin-1/2 system are studied. It is shown that for the AC case the correlation function of the Clauser-Horne-Shimony-Holt (CHSH) inequality for certain choices of the spin measurements depends on the AC phase explicitly.