Quantum phase transition in symmetric quantum three-body system

Abstract

Bound state energy (E) and the position (\n $$E_r$$\n ) and width (\n $$\\Gamma $$\n ) of the first S symmetry doubly excited Feshbach resonance state of various symmetrical three-body systems (XYY) bound via screened Coulomb (SC) interaction have been reported using soft-wall strategy of stabilization method. Explicitly correlated multi-exponent Hylleraas-type basis set has been considered under the Ritz variational framework. Critical nuclear charges of the systems in its ground state (\n $$Z_c$$\n ) as well as in Feshbach resonance state (\n $${\\mathcal {Z}}_c$$\n ) for various screening parameters (\n $$\\lambda $$\n ) have been evaluated. First-order quantum phase transition (QPT) for all the systems has been reported in its ground state. Effect of different mass combination of the constituents particles on critical points of the systems has been explored extensively.