Detailed analysis of quantum phase transitions within the $u(2)$ algebra

TL;DR

This paper provides a detailed analysis of quantum phase transitions in $u(2)$ algebraic models for bosonic systems, exploring transitions between dynamical symmetries and effects of higher-order Hamiltonian terms.

Contribution

It introduces a comprehensive study of phase transitions in $u(2)$ models, including exact diagonalization and the impact of higher-order Hamiltonian terms.

Findings

Quantum phase transitions occur between $u(1)$ and $so(2)$ symmetry chains.

Higher-order Hamiltonian terms can induce similar phase transitions within a single chain.

Exact diagonalization and coherent state methods effectively analyze these transitions.

Abstract

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 $u(2)\supset u(1)$ and $u(2)\supset so(2)$ 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.