# Quantum phase transitions in the interacting boson model: integrability, level repulsion, and level crossing.

@article{Arias2003QuantumPT, title={Quantum phase transitions in the interacting boson model: integrability, level repulsion, and level crossing.}, author={J. M. Arias and Jorge Dukelsky and Jos{\'e} Enrique Garcı́a-Ramos}, journal={Physical review letters}, year={2003}, volume={91 16}, pages={ 162502 } }

We study the quantum phase transition mechanisms that arise in the interacting boson model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.

## 36 Citations

Quantum phase transitions in the consistent-Q Hamiltonian of the interacting boson model

- Physics
- 2008

Quantum phase transitional patterns in the whole parameter space of the consistent-Q Hamiltonian in the interacting boson model are studied based on an implemented Fortran code for the numerical…

QUANTUM PHASE TRANSITIONAL BEHAVIOR IN THE EXTENDED CASTEN TRIANGLE OF THE INTERACTING BOSON MODEL

- Physics
- 2006

Quantum phase transitional patterns in the whole parameter space of the consistent-Q Hamiltonian in the Interacting Boson Model are studied based on an implemented Fortran code for numerical…

Lie algebra symmetries and quantum phase transitions in nuclei

- Physics
- 2014

In this paper, an overview of some aspects of quantum phase transitions (QPT) in nuclei is given and they are: (i) QPT in interacting boson model (sdIBM), (ii) QPT in two-level models, (iii) critical…

Quantum phase transitions in the interacting boson model

- Physics
- 2009

Abstract This review is focused on various properties of quantum phase transitions (QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model describes collective modes of motions in…

Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. I. Level dynamics

- Physics
- 2006

We investigate the evolution of quantal spectra and the corresponding wave functions along the [O(6)-U(5)] superset of O(5) transition of the interacting boson model. The model is integrable in this…

Finite-size scaling exponents in the interacting boson model

- Physics
- 2005

We investigate the finite-size scaling exponents for the critical point at the shape-phase transition from U(5) (spherical) to O(6) (deformed {gamma}-unstable) dynamical symmetries of the interacting…

Quantum phase crossovers with finite atom number in the Dicke model

- Physics
- 2013

Two-level atoms interacting with a one-mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom–cavity…

An Alternative Description of the Prolate-Oblate Shape Phase Transition in the Interacting Boson Model

- Physics
- 2013

The prolate-oblate shape phase transition in the interacting boson model is investigated for finite N as well as in the large-N classical limit by adopting the Hamiltonian with a linear dependence on…

Phase transitions and quasi-dynamical symmetry in nuclear collective models, III: The U(5) to SU(3) phase transition in the IBM

- Physics
- 2004

Abstract This paper studies the dependence of the U(5) to SU(3) phase transition in the interacting boson model (IBM) on the finite number N of bosons. Such investigations illuminate the relationship…

Some observables as an indication of atomic nuclear shape phase transition

- Physics
- 2007

Using interacting boson model, shape phase transitions from U(5) to O(6) and from U(5) to SU(3) are studied in the space of two control parameters. Some simple shape phase diagrams in terms of the…

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