Physical Review C

Alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model

L. R. Dai, Feng Pan, L. Liu, L. X. Wang, Jerry Paul Draayer

Published Sep 13, 2012• 7 citations

Abstract

The quantum phase transitional behavior of an alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model is explored. Specifically, the usual SU(3) quadrupole-quadrupole interaction is replaced by an O(6) cubic interaction, and the transitional behaviors of the low-lying energy levels, eigenstates, isomer shifts, $E$2 transition rates, and expectation values of shape variables across the entire transitional region are all examined within this context. A comparison with outcomes of the usual U(5)-SU(3) transitional description shows that the spherical to axially deformed shape-phase transition can also be described within this alternative context, especially near the critical point. However, with the O(6) cubic interaction the transition is considerably smoother than for the U(5)-SU(3) case, but with the nuclear shape less well defined, even in the axially deformed limit. It is also shown that the new scheme seems better than the usual U(5)-SU(3) scheme in describing the low-lying spectrum of ${}^{152}$Sm with X(5) critical point symmetry.

DOI: 10.1103/physrevc.86.034316

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Physical Review C

Alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model

L. R. Dai, Feng Pan, L. Liu, L. X. Wang, Jerry Paul Draayer

Published Sep 13, 2012• 7 citations

Publisher

Abstract

E

2 transition rates, and expectation values of shape variables across the entire transitional region are all examined within this context. A comparison with outcomes of the usual U(5)-SU(3) transitional description shows that the spherical to axially deformed shape-phase transition can also be described within this alternative context, especially near the critical point. However, with the O(6) cubic interaction the transition is considerably smoother than for the U(5)-SU(3) case, but with the nuclear shape less well defined, even in the axially deformed limit. It is also shown that the new scheme seems better than the usual U(5)-SU(3) scheme in describing the low-lying spectrum of

{}^{152}

Sm with X(5) critical point symmetry.

DOI: 10.1103/physrevc.86.034316

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E

{}^{152}

Sm with X(5) critical point symmetry.

Symmetry-Reduced Variational Quantum Simulation of the

U(5)\rightarrow SU(3)

Quantum Phase Transition in the Interacting Boson Model

The spherical-to-deformed quantum phase transition of the Interacting Boson Model (IBM) is investigated using the variational quantum eigensolver (VQE). The

U(5)

SU(3)

transitional Hamiltonian is studied with

χ=-\sqrt{7}/2

. We develop a symmetry-preserving, minimum-qubit VQE framework for collective nuclear models, achieving a substantial reduction in qubit requirements without compromising the finite-size quantum-phase-transition physics. The transition is characterized through the normalized

d

-boson occupation and ground-state energy derivatives. Finite-size results are found to approach the analytic critical point

ξ_c=8/17\simeq0.470588

, with an independent order-parameter extrapolation yielding

ξ_\infty=0.46986(61)

. The VQE reproduces ground-state energies and structural observables to numerical precision. These results demonstrate the potential of symmetry-reduced VQE for efficient quantum simulations of collective nuclear dynamics and quantum phase transitions.

The quantum-phase-transitional behavior of the spherical shell-model mean field plus the geometric quadrupole-quadrupole and standard pairing model within a single-

j

shell is analyzed in detail. Various quantities, such as low-lying energy levels, some typical energy ratios, the overlaps of the excited states with those of the corresponding limiting cases,

B(E2)

values and electric quadrupole moments of some low-lying states and their ratios, as functions of the control parameter of the model in a

j=15/2

shell are calculated as an example, in which only a crossover occurs due to the Pauli exclusion. The results show that there are noticeable changes within the crossover region of the rotation-like to the pair-excitation (superconducting) phase transition, especially in the half-filling case. As an application to realistic nuclear systems, a chain of isotones $^{212}\mathrm{Rn}\text{\ensuremath{-}}^{213}\mathrm{Fr}\text{\ensuremath{-}}^{214}\mathrm{Ra}\text{\ensuremath{-}}^{215}\mathrm{Ac}$ is chosen to be described by the model with valence protons in the

1{h}_{9/2}

shell. As far as the low-lying energy levels, the experimentally observed

B(E2)

values, and the electric quadrupole moment within the yrast band are concerned, these nuclei seem fitted reasonably well. The results indicate that these nuclei are all within the rotation-like to the pair-excitation phase transition near the crossover point.

We study quantum phase transitions between spherical, prolate, and oblate nuclear ground-state shapes using the interacting

\mathrm{sd}

-boson model

(sd

-IBM) and demonstrate the analogy between the IBM results (also results of any axially symmetric quadrupole collective model) and predictions of the Landau theory of phase transitions in classical thermodynamics. A detailed comparison of the two frameworks is performed exploiting the concept of ``specific heat,'' introduced in four alternative ways in the quantum case. All these definitions (two of them based on spectroscopic features of the ground state, the others on a randomized version of the model) lead to similar peaked forms of the ``specific heat'' at the point of the quantum phase transition. We analyze the effect of an increasing boson number on these curves and observe convergence to the singular phase-transitional behavior in the classical limit. Other observable signatures of the IBM structural phase transitions are also discussed with the aim to facilitate the location of a particular nucleus in the parameter space (extended Casten triangle) near the transitions.