Quantum phase transitions in an effective Hamiltonian: fast and slow systems

TL;DR

This paper derives an effective Hamiltonian for fast and slow quantum systems in strong interaction regimes and investigates quantum phase transitions as ground state bifurcations, with applications to atom-field and atom-atom interactions.

Contribution

It introduces a new effective Hamiltonian framework for coupled fast-slow quantum systems and analyzes quantum phase transitions as bifurcations of the ground state.

Findings

Effective Hamiltonian derived for strong interaction limit

Quantum phase transition identified as ground state bifurcation

Applications demonstrated in atom-field and atom-atom systems

Abstract

An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the ground state of the "slow subsystem" in the thermodynamic limit. Examples as atom-field and atom-atom interactions are analyzed in detail.