Tricritical point in the quantum Hamiltonian mean-field model

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 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.

Exact mean-field solution of a spin chain with short-range and long-range interactions

“…The model we study has itself appeared in different contexts, such as particle-numberconserving version the Kitaev wire model [19], power-law interactions with exponent smaller than 1 [8,20,21], or in models of quantum optics at zero temperature [22]. Celebrated models with all-to-all interactions are the Curie-Weiss model [23] and the Lipkin-Meshkov-Glick model [24], and different models with all-to-all interactions have attracted attention recently [25][26][27][28][29].…”