Finite-size scaling exponents in the interacting boson model

Abstract

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 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 $E2$ transition probability from the ground state to the first excited state, and determine the corresponding finite-size scaling exponents.

arXiv comment4 pages, 3 figures, published version

References in corpus (10)

• Quantum phase transitions
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
• Quantum phase transition in an atomic Bose gas with a Feshbach resonance
• The U(5)-O(6) transition in the Interacting Boson Model and the E(5) critical point symmetry
• Quantum Phase Transitions in the Interacting Boson Model: Integrability, level repulsion and level crossing
• Condensate Fragmentation in a New Exactly Solvable Model for Confined Bosons
• Finite-size scaling exponents and entanglement in the two-level BCS model
• New mechanism for the enhancement of $sd$ dominance in interacting boson models

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• Effect of a fermion on quantum phase transitions in bosonic systems
• Flow Equations and Normal Ordering. A Survey
• Phase diagram for a Cubic Consistent-Q Interacting Boson Model Hamiltonian: signs of triaxiality
• Two-level interacting boson models beyond the mean field
• Dual algebraic structures for the two-level pairing model
• A scalar two-level boson model to study the IBM phase diagram in the Casten triangle
• Continuous unitary transformations in two-level boson systems
• First-Order Quantum Phase Transition in a Finite System
• First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries
• The emergent dynamical symmetry at the triple point of nuclear deformations
• Quantum catastrophes from an algebraic perspective
• On the Geodesic Nature of Wegner's Flow