arXiv:cond-mat/0509721 · Physical Review C

Continuous unitary transformations in two-level boson systems

Sébastien Dusuel, Julien Vidal, J. M. Arias, J. Dukelsky, J. E. García-Ramos

Published Dec 30, 2005• 39 citations

Abstract

Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out. Analytical results beyond the simple mean-field treatment are deduced by using the continuous unitary transformations technique. In this scheme, a $1/N$ expansion for different observables is proposed and allows one to compute the finite-size scaling exponents at the critical point. Analytical and numerical results are compared and reveal the power of the present approach to compute the finite-size corrections in such a context.

DOI: 10.1103/physrevc.72.064332

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arXiv:cond-mat/0509721 · Physical Review C

Continuous unitary transformations in two-level boson systems

Sébastien Dusuel, Julien Vidal, J. M. Arias, J. Dukelsky, J. E. García-Ramos

Published Dec 30, 2005• 39 citations

arXiv HTML PDF

Abstract

Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with

O(2L+1)

symmetry for large number of bosons is worked out. Analytical results beyond the simple mean-field treatment are deduced by using the continuous unitary transformations technique. In this scheme, a

1/N

expansion for different observables is proposed and allows one to compute the finite-size scaling exponents at the critical point. Analytical and numerical results are compared and reveal the power of the present approach to compute the finite-size corrections in such a context.

DOI: 10.1103/physrevc.72.064332

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Symmetry-Reduced Variational Quantum Simulation of the $U(5)\rightarrow SU(3)$ Quantum Phase Transition in the Interacting Boson ModelSymmetry-Reduced Variational Quantum Simulation of the $U(5)\rightarrow SU(3)$ Quantum Phase Transition in the Interacting Boson Model

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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 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.

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Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with

O(2L+1)

symmetry for large number of bosons is worked out. Analytical results beyond the simple mean-field treatment are deduced by using the continuous unitary transformations technique. In this scheme, a

1/N

E2

transition probability from the ground state to the first excited state and determine the corresponding finite-size scaling exponents.

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.