Sign problem free quantum Monte-Carlo study on thermodynamic properties and magnetic phase transitions in orbital-active itinerant ferromagnets

TL;DR

This study uses sign-problem-free quantum Monte Carlo simulations to investigate thermodynamic properties and magnetic phase transitions in a two-dimensional multi-orbital Hubbard model, revealing key insights into itinerant ferromagnetism.

Contribution

It provides the first non-perturbative, sign-problem-free quantum Monte Carlo analysis of ferromagnetic transitions in multi-orbital systems, elucidating the roles of Hund's coupling and electron itinerancy.

Findings

Ferromagnetic ground states are stabilized by Hund's coupling and electron itinerancy.

Spin susceptibility exhibits Curie-Weiss behavior and exponential growth near zero temperature.

Long-range ferromagnetic order occurs when symmetry is reduced to Ising class.

Abstract

The microscopic mechanism of itinerant ferromagnetism is a long-standing problem due to the lack of non-perturbative methods to handle strong magnetic fluctuations of itinerant electrons. We have non-pertubatively studied thermodynamic properties and magnetic phase transitions of a two-dimensional multi-orbital Hubbard model exhibiting ferromagnetic ground states. Quantum Monte-Carlo simulations are employed, which are proved in a wide density region free of the sign problem usually suffered by simulations for fermions. Both Hund's coupling and electron itinerancy are essential for establishing the ferromagnetic coherence. No local magnetic moments exist in the system as a priori, nevertheless, the spin channel remains incoherent showing the Curie-Weiss type spin magnetic susceptibility down to very low temperatures at which the charge channel is already coherent exhibiting a weakly temperature-dependent compressibility. For the SU(2) invariant systems, the spin susceptibility further grows exponentially as approaching zero temperature in two dimensions. In the paramagnetic phase close to the Curie temperature, the momentum space Fermi distributions exhibit strong resemblance to those in the fully polarized state. The long-range ferromagnetic ordering appears when the symmetry is reduced to the Ising class, and the Curie temperature is accurately determined. These simulations provide helpful guidance to searching for novel ferromagnetic materials in both strongly correlated $d$-orbital transition metal oxide layers and the $p$-orbital ultra-cold atom optical lattice systems.