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.
The author has studied the influence of fermion-boson conversion on Mott states near Feshbach resonances. It is demonstrated that Mott states are unstable with respect to fermion-boson conversion. A branch of collective modes in superfluids has been found, which involve antisymmetric phase oscillations in fermionic and bosonic channels and are always gapped. The low-energy quantum dynamics of a Fermi-Bose superfluid can be fully characterized by either an effective coupled $\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{U}(1)$ quantum rotor Hamiltonian or a coupled $XXZ\ensuremath{\bigotimes}XXZ$ spin model.
Abstract The effect of unstable quasiparticles in the out-of-equilibrium dynamics of certain integrable systems has been the subject of several recent studies. In this paper we focus on the stationary value of the entanglement entropy density, its growth rate, and related functions, after a quantum quench. We consider several quenches, each of which is characterised by a corresponding squeezed coherent state. In the quench action approach, the coherent state amplitudes K(θ) become input data that fully characterise the large-time stationary state, thus also the corresponding Yang-Yang entropy. We find that, as function of the mass of the unstable particle, the entropy growth rate has a global minimum signalling the depletion of entropy that accompanies a slowdown of stable quasiparticles at the threshold for the formation of an unstable excitation. We also observe a separation of scales governed by the interplay between the mass of the unstable particle and the quench parameter, separating a non-interacting regime described by free fermions from an interacting regime where the unstable particle is present. This separation of scales leads to a double-plateau structure of many functions, where the relative height of the plateaux is related to the ratio of central charges of the UV fixed points associated with the two regimes, in full agreement with conformal field theory predictions. The properties of several other functions of the entropy and its growth rate are also studied in detail, both for fixed quench parameter and varying unstable particle mass and viceversa.