The spherical to γ-unstable quantum shape-phase transition (QPT) is explored in the framework of the interacting boson model (IBM), with special emphasis on the critical point. Up to now, only one- and two-body Hamiltonians were employed to describe this QPT, and it was necessarily second-order without shape coexistence. In this work, we show that with the use of a three-body Hamiltonian the QPT can become first-order [1]. We do that by introducing the general three-body Hamiltonian and construct the three-body energy surface which is independent of γ. We then identify the conditions for a first- and second- order transition and obtain the complete phase diagram. Next, we consider two approaches for identifying Hamiltonians which are appropriate for a first-order QPT, (i) complete approach employing one-, two- and three-body interactions which describe the entire QPT and (ii) resolution of the Hamiltonian into intrinsic and collective parts at the critical point. In the first approach, we identify spectral signatures along the critical line. In the second approach, we examine the role of the energy barrier and the presence of partial symmetries in the intrinsic part. A detailed analysis of the spectrum and E2 transitions is carried in both approaches.

[1] Noam Gavrielov. A First-Order Quantum Phase Transition Between Spherical and γ-Unstable Nuclear Shapes from an Algebraic Perspective. Master’s thesis, The Hebrew University, Jerusalem (2015).