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arXiv:nucl-th/0507038 · Physical Review C

β4 potential at the U(5)–O(6) critical point of the interacting boson model

J. E. García-Ramos, J. Dukelsky, J. M. Arias

Published Sep 8, 2005• 32 citations
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Abstract

Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form that can be diagonalized for large number of bosons. We present results for the low-energy spectrum and the transition probabilities for systems up to 10,000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a ${\ensuremath{\beta}}^{4}$ potential.

DOI
10.1103/physrevc.72.037301

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Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form that can be diagonalized for large number of bosons. We present results for the low-energy spectrum and the transition probabilities for systems up to 10,000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a \ensuremathβ4{\ensuremath{\beta}}^{4}\ensuremathβ4 potential.
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The U (5)– O (6) transitional behaviour of the interacting Boson model in the large- N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B ( E 2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviours of these quantities are greatly enhanced with an increase in the total number of bosons N ; in particular, the fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n d in the first excited 0 + state and the ground state, and another quantity related to the isomer shift behave similarly in both the O (6)– U (5) large- N and U (5)– SU (3) phase transitions.
Symmetry-Reduced Variational Quantum Simulation of the U(5)→SU(3)U(5)\rightarrow SU(3)U(5)→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)U(5)U(5)--SU(3)SU(3)SU(3) transitional Hamiltonian is studied with χ=−7/2χ=-\sqrt{7}/2χ=−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 ddd-boson occupation and ground-state energy derivatives. Finite-size results are found to approach the analytic critical point ξc=8/17≃0.470588ξ_c=8/17\simeq0.470588ξc​=8/17≃0.470588, with an independent order-parameter extrapolation yielding ξ∞=0.46986(61)ξ_\infty=0.46986(61)ξ∞​=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 investigate the finite-size scaling exponents for the critical point at the shape-phase transition from U(5) (spherical) to O(6) (deformed \ensuremath{\gamma}-unstable) dynamical symmetries of the interacting boson model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading-order correction to the ground-state energy, the gap, the expectation value of the d-boson number in the ground state and the E2E2E2 transition probability from the ground state to the first excited state and determine the corresponding finite-size scaling exponents.
We investigate the evolution of quantal spectra and the corresponding wave functions along the [O(6)-U(5)] \ensuremath{\supset} O(5) transition of the interacting boson model. The model is integrable in this regime, and its ground state passes through a second-order structural phase transition. We show that the whole spectrum as a function of the Hamiltonian control parameter as well as structures of all excited states exhibit rather organized and correlated behaviors, which provide deeper insight into the nature of this transitional path.