Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and Theoretical

Phase structure of interacting boson models in arbitrary dimension

Pavel Cejnar, FRANCESCO IACHELLO

Published Jan 9, 2007• 72 citations
Publisher

Abstract

We analyse the phase structure of a class of interacting boson models with two types of bosons, one scalar and one non-scalar, subject to one- and two-body interactions and with dynamic algebra U(n). To these models, we associate a classical description in terms of f = n − 1 variables. We show that, if the system is invariant under two- or three-dimensional rotations (for f ≥ 2 even or odd), the models have both first- and second-order phase transitions only if f = 5, 9, 13, .... In the other f ≥ 2 cases, the system has only second-order transitions. All phase transitions of this class of models belong to the cusp catastrophe in the classification of structurally unstable potentials.

DOI
10.1088/1751-8113/40/4/001

Related papers

Quantum catastrophes from an algebraic perspective

A. Leviatan, N. Gavrielov

Abstract We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The analysis employs an interacting boson model Hamiltonian describing quantum phase transitions between specific quadrupole shapes by interpolating between two incompatible dynamical symmetry limits. The classical properties are determined by using coherent states to construct the complete phase diagrams associated with Landau potentials exhibiting such catastrophes. The quantum properties are determined by analyzing the spectra, transition rates and symmetry character of the eigenstates of critical Hamiltonians.

arXiv:2008.13717•Journal of Physics Conference Series•Aug 1, 2020•4 citations

Detailed Analysis of Quantum Phase Transitions Within theu(2) Algebra

L. Fortunato, L Sartori

We analyze in detail the quantum phase transitions that arise in models based on the u (2) algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains u (2)⊃ u (1) and u (2) ⊃so(2) by diagonalizing the problem exactly in the u(1) basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a single chain just by including higher order terms in the hamiltonian.

arXiv:0910.2341•Communications in Theoretical Physics•Oct 1, 2010•3 citations

Excited-state quantum phase transitions in systems with two degrees of freedom. III. Interacting boson systems

Michal Macek, Pavel Stránský, A. Leviatan +1 more

The series of articles [Ann. Phys. 345, 73 (2014) and Ann. Phys. 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with $f=2$ degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. The intrinsic Hamiltonian formalism with angular momentum fixed to $L=0$ is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a nontrivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.

arXiv:1903.10234•Physical Review C•Jun 21, 2019•38 citations

Investigation of Structure and Nuclear Shape Phase Transition in Odd Nuclei in a multi-j model

Ameneh Kargarian, Maryam Ghapanvari

In this paper‎, ‎we study the nature of the dynamics in second-order Quantum Phase Transition (QPT) between vibrational ( ) and -unstable ( ) nuclear shapes‎. ‎Using a transitional Hamiltonian according to an affine SU(1,1) algebra in combination with a coherent state formalism, Shape Phase Transitions (SPT) in odd-nuclei in the framework of the Interacting Boson Fermion Model (IBFM) are investigated‎. ‎Classical analysis reveals a change in the system along with the transition in a critical point‎. ‎The role of a fermion with angular momentum j at the critical point on quantum phase transitions in bosonic systems is investigated via a semi-classical approach‎. ‎The effect of the coupling of the odd particle to an even-even boson core is discussed along with the shape transition and‎, ‎in particular‎, ‎at the critical point‎. Our study confirms the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and determine the critical point's precise position‎.

Journal of Nuclear Research and Applications•Jun 1, 2022•0 citations

Spin-spin coupling-based quantum and classical phase transitions in two-impurity spin-boson models

Roberto Grimaudo, ANTONINO MESSINA, Hiromichi Nakazato +2 more

The class of two-interacting-impurity spin-boson models with vanishing transverse fields on the spin-pair is studied. The model can be exactly mapped into two independent standard single-impurity spin-boson models where the role of the tunnelling parameter is played by the spin-spin coupling. The dynamics of the magnetization is analysed for different levels of (an)isotropy. Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light.

arXiv:2205.09367•May 19, 2022•0 citations

TheE(2) symmetry and quantum phase transition in the two-dimensional limit of the vibron model

Yu Zhang, Feng Pan, Yu-xin Liu +1 more

We study in detail the relation between the two-dimensional Euclidean dynamical E(2) symmetry and the quantum phase transition in the two-dimensional limit of the vibron model, called the U(3) vibron model. Both geometric and algebraic descriptions of the U(3) vibron model show that structures of low-lying states at the critical point of the model with a quartic potential as its classical limit can be approximately described by the E(2) symmetry. We also fit the finite-size scaling exponent of the energy levels and E1 transition rates in the F(2) model, which is exactly the E(2) model but with truncation in its Hilbert subspace, as well as those at the critical point in the U(3) vibron model. The N-scaling power law around the critical point shows that the E(2) symmetry is well preserved even for cases with finite number of bosons. In addition, two kinds of experimentally accessible effective order parameters, such as the energy ratios E21/E11, E31/E 11 and E1 transition ratios B(E1;21→1 1)/B(E1;11→11), B(E1;02→ 11)/B(E1;11→01), are proposed to identify the second-order phase transition in such systems. Possible empirical examples exhibiting approximate E(2) symmetry are also presented. © 2010 IOP Publishing Ltd.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 29, 2010•9 citations
We analyse the phase structure of a class of interacting boson models with two types of bosons, one scalar and one non-scalar, subject to one- and two-body interactions and with dynamic algebra U(n). To these models, we associate a classical description in terms of f = n − 1 variables. We show that, if the system is invariant under two- or three-dimensional rotations (for f ≥ 2 even or odd), the models have both first- and second-order phase transitions only if f = 5, 9, 13, .... In the other f ≥ 2 cases, the system has only second-order transitions. All phase transitions of this class of models belong to the cusp catastrophe in the classification of structurally unstable potentials.
Abstract We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The analysis employs an interacting boson model Hamiltonian describing quantum phase transitions between specific quadrupole shapes by interpolating between two incompatible dynamical symmetry limits. The classical properties are determined by using coherent states to construct the complete phase diagrams associated with Landau potentials exhibiting such catastrophes. The quantum properties are determined by analyzing the spectra, transition rates and symmetry character of the eigenstates of critical Hamiltonians.
We analyze in detail the quantum phase transitions that arise in models based on the u (2) algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains u (2)⊃ u (1) and u (2) ⊃so(2) by diagonalizing the problem exactly in the u(1) basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a single chain just by including higher order terms in the hamiltonian.
The series of articles [Ann. Phys. 345, 73 (2014) and Ann. Phys. 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with f=2f=2f=2 degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. The intrinsic Hamiltonian formalism with angular momentum fixed to L=0L=0L=0 is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a nontrivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.
In this paper‎, ‎we study the nature of the dynamics in second-order Quantum Phase Transition (QPT) between vibrational ( ) and -unstable ( ) nuclear shapes‎. ‎Using a transitional Hamiltonian according to an affine SU(1,1) algebra in combination with a coherent state formalism, Shape Phase Transitions (SPT) in odd-nuclei in the framework of the Interacting Boson Fermion Model (IBFM) are investigated‎. ‎Classical analysis reveals a change in the system along with the transition in a critical point‎. ‎The role of a fermion with angular momentum j at the critical point on quantum phase transitions in bosonic systems is investigated via a semi-classical approach‎. ‎The effect of the coupling of the odd particle to an even-even boson core is discussed along with the shape transition and‎, ‎in particular‎, ‎at the critical point‎. Our study confirms the importance of the odd nuclei as necessary signatures to characterize the occurrence of the phase transition and determine the critical point's precise position‎.
The class of two-interacting-impurity spin-boson models with vanishing transverse fields on the spin-pair is studied. The model can be exactly mapped into two independent standard single-impurity spin-boson models where the role of the tunnelling parameter is played by the spin-spin coupling. The dynamics of the magnetization is analysed for different levels of (an)isotropy. Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light.
We study in detail the relation between the two-dimensional Euclidean dynamical E(2) symmetry and the quantum phase transition in the two-dimensional limit of the vibron model, called the U(3) vibron model. Both geometric and algebraic descriptions of the U(3) vibron model show that structures of low-lying states at the critical point of the model with a quartic potential as its classical limit can be approximately described by the E(2) symmetry. We also fit the finite-size scaling exponent of the energy levels and E1 transition rates in the F(2) model, which is exactly the E(2) model but with truncation in its Hilbert subspace, as well as those at the critical point in the U(3) vibron model. The N-scaling power law around the critical point shows that the E(2) symmetry is well preserved even for cases with finite number of bosons. In addition, two kinds of experimentally accessible effective order parameters, such as the energy ratios E21/E11, E31/E 11 and E1 transition ratios B(E1;21→1 1)/B(E1;11→11), B(E1;02→ 11)/B(E1;11→01), are proposed to identify the second-order phase transition in such systems. Possible empirical examples exhibiting approximate E(2) symmetry are also presented. © 2010 IOP Publishing Ltd.