Itinerant ferromagnetism (FM), .e., FM of mobile electrons with
Fermi surfaces, is one of the major challenges of contemporary
condensed-matter physics.
Unlike superconductivity, which has a well-controlled weak-coupling
Bardeen-Cooper-Schrieffer theory as a starting point, itinerant
FM is an intrinsically strong correlation phenomenon.
The Stoner criterion neglects correlation effects and thus overestimates the
FM tendency.
FM is favored by repulsive interactions, however, and even under very
strong repulsions electrons typically still remain unpolarized because
of the large kinetic energy cost required for spin polarizations.
In particular, the finite temperature thermodynamic properties and
magnetic phase transitions are long-standing problems of itinerant
FM characterized by strong dynamic fluctuations of ferromagnetic
domains.
These difficulties are typically beyond the scope of perturbative
methods.
We conduct a nonperturbative study of itinerant FM by proving
exact theorems and by using sign-problem free quantum Monte Carlo
simulations.
Our study provides a well-controlled benchmark and guidance for
the study of the mechanism of itinerant FM and for
current experimental efforts to search for novel FM
states in both condensed matter and ultracold atom systems.
Theorems for the ground state itinerant ferromagnetism
In spite of these difficulties, we have made a significant progress
in proving a series of theorems on the existence of the ground state
itinerant FM.
Different from the Nagaoka theorem which only applies to a single-hole,
our theorem establishes a FM phase over a large region of electron fillings
in strongly correlated multi-orbital bands
[Ref. 1] .
Our theorems proved that Hund's rule combined with the quasi-1D band
structure lead to the 2D and 3D FM long-range orders
in the strong coupling regime.
Curie-Weiss metal phase and sign-problem free QMC simulations
It is not only difficult to prove the ground state FM, but also the
the Curie-Weiss (CW) metal phase is also a long-standing problem
exhibiting a dichotomic nature: The spin channel is local moment-like
and incoherent while the charge channel remains coherent showing the
existence of Fermi surfaces.
The method of quantum Monte Carlo simulations is ideal for studying strongly correlated systems, and it produces asymptotically exact results. However, it typically suffers from the sign problem in fermion systems, which leads to uncontrollable numerical errors. Performing sign-problem-free quantum Monte Carlo simulations for itinerant fermion systems and ferromagnetic phase transitions is a significant challenge in strong correlation physics. We demonstrate a remarkable property of a multiorbital Hubbard model possessing ferromagnetic ground states: The sign problem is absent for all of the filling densities at any temperatures [Ref. 2] . This fact opens up new opportunities for well-controlled studies of the thermodynamics of itinerant ferromagnetism with asymptotic exactness.
We performed QMC simulations on the magnetic phase diagram and the Curie-Weiss metal state [Ref. 2] . The simulation unambiguously shows although no local magnetic moments exist as a priori, 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 weakly temperature-dependent compressibility. The critical scalings of magnetic phase transitions were performed based on which Curie temperatures were obtained with high numeric precision. In the Curie-Weiss metal phase, the momentum space Fermi distributions are signficiantly distorted from the weak-interacting unpolarized Fermi surface, but resemble those in the fully polarized states.
Application to experimental systems
These models are nearly realistic, and pertinent to experiments. Especially, our study pro-
vides important guidance to the study of novel FM materials in transition-metal-oxides (e.g.
SrTiO3/LaAlO3interface) and ultra-cold atom optical lattices (e.g. the p-orbital bands
References and talks
Phys. Rev. Lett. 112, 217201 (2014) . See pdf file .
Phys. Rev. X 5, 021032, (2015) .
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Last modified: July 15, 2007.