Continuous unitary transformations in two-level boson systems

TL;DR

This paper develops a formalism using continuous unitary transformations to analyze two-level boson systems undergoing quantum phase transitions, enabling precise finite-size scaling analysis beyond mean-field approximations.

Contribution

It introduces a novel approach employing continuous unitary transformations and 1/N expansion to diagonalize Hamiltonians with high symmetry in large boson systems, providing analytical and numerical insights.

Findings

Effective computation of finite-size scaling exponents at criticality.

Validation of analytical results with numerical simulations.

Enhanced understanding of quantum phase transitions in boson systems.

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.