Tricritical point in the quantum Hamiltonian mean-field model

Area of Science:

• Quantum physics
• Condensed matter theory
• Statistical mechanics

Background:

• Recent advancements in engineering long-range interactions in diverse quantum systems.
• The success of classical Hamiltonian mean-field models in describing collective phenomena.

Purpose of the Study:

• To generalize the classical Hamiltonian mean-field model to fermionic particles.
• To investigate the phase diagram and thermodynamic properties of this generalized model.
• To explore quantum phase transitions and tricriticality in systems with long-range interactions.

Main Methods:

• Generalization of the classical Hamiltonian mean-field model for fermionic systems.
• Canonical ensemble analysis.
• Investigation as a function of temperature and hopping.
• Exact diagonalization.
• Mean-field theory.

Main Results:

• At zero temperature, quantum phase transition from ordered to disordered phase driven by charge fluctuations.
• At higher temperatures, phase transition is initially first-order.
• A tricritical point is identified where the transition switches to second-order.
• Demonstration of tricriticality in a quantum system with long-range couplings.

Conclusions:

• The generalized model provides an intriguing example of tricriticality in quantum systems.
• The findings have direct relevance for experimental quantum systems with long-range couplings.
• Charge fluctuations play a crucial role in driving quantum phase transitions.