Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path.
Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-
A nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine
SU(1,1) Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-
A are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of
122−−134Xe,102−−110Pd, and
123−−133Xe were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum
j to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.
We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via
s-wave Feshbach resonance and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor ${\ensuremath{\nu}}_{f}=2$. We show that the system undergoes a continuous quantum phase transition from a ${\ensuremath{\nu}}_{f}=2$ fermionic integer quantum Hall state formed by atoms to a ${\ensuremath{\nu}}_{b}=1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field-theoretical predictions and the case of
p-wave pairing.