Journal of Physics G Nuclear and Particle Physics

Investigation of quantum phase transitions in the spdf interacting boson model based on dual algebraic structures for the four-level pairing model

M. A. Jafarizadeh, Amir Jalili, N. Fouladi, Maryam Ghapanvari

Published Aug 18, 2016• 20 citations

Abstract

Abstract The building blocks of the interacting boson model (IBM) are associated with both s and d bosons for positive parity states. An extension of sd −IBM along these models to spdf −IBM can provide the appropriate framework to describe negative parity states. In this paper, a solvable extended transitional Hamiltonian based on the affine SU ( 1 , 1 ) ^ Lie algebra is proposed to describe low lying positive and negative parity states between the spherical and deformed gamma-unstable shape. Quantum phase transitions (QPTs) are investigated based on dual algebraic structures for the four-level pairing model. Numerical extraction to low-lying energy levels and transition rates within the control parameters of this evaluated Hamiltonian are presented for various N values. By reproducing the experimental results, the method based on the signatures of the phase transition, such as the expectation value of the boson number operators in the lowest excited states, are used to provide a better description of Ru isotopes in this transitional region.

DOI: 10.1088/0954-3899/43/9/095108

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Journal of Physics G Nuclear and Particle Physics

Investigation of quantum phase transitions in the spdf interacting boson model based on dual algebraic structures for the four-level pairing model

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Published Aug 18, 2016• 20 citations

Publisher

Abstract

DOI: 10.1088/0954-3899/43/9/095108

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{}^{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.

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.