Finite-size scaling exponents in the interacting boson model

TL;DR

This paper analyzes the finite-size scaling exponents at the critical point of a shape phase transition in the Interacting Boson Model, using advanced mathematical techniques to compute key physical quantities.

Contribution

It provides exact calculations of leading order corrections and finite-size scaling exponents for the U(5) to O(6) transition in the Interacting Boson Model.

Findings

Exact leading order corrections to ground state energy and gap.

Finite-size scaling exponents for $d$-boson number and $E2$ transition probability.

Methodology applicable to other quantum phase transition studies.

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.