Tricritical point in the quantum Hamiltonian mean-field model

TL;DR

This paper investigates a quantum extension of the classical Hamiltonian mean-field model, revealing a tricritical point where the phase transition changes from first to second order, with implications for long-range interacting quantum systems.

Contribution

It introduces a quantum fermionic version of the classical model and characterizes its phase diagram, highlighting the presence of a tricritical point in the quantum regime.

Findings

First-order quantum phase transition at zero temperature.

Existence of a tricritical point where transition order changes.

Exact diagonalization and mean-field theory confirm results.

Abstract

Engineering long-range interactions in experimental platforms has been achieved with great success in a large variety of quantum systems in recent years. Inspired by this progress, we propose a generalization of the classical Hamiltonian mean-field model to fermionic particles. We study the phase diagram and thermodynamic properties of the model in the canonical ensemble for ferromagnetic interactions as a function of temperature and hopping. At zero temperature, small charge fluctuations drive the many-body system through a first order quantum phase transition from an ordered to a disordered phase at zero temperature. At higher temperatures, the fluctuation-induced phase transition remains first order initially and switches to second order only at a tricritical point. Our results offer an intriguing example of tricriticality in a quantum system with long-range couplings, which bears direct experimental relevance. The analysis is performed by exact diagonalization and mean-field theory.