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

摘要

The microscopic mechanism of itinerant ferromagnetism is a long-standingproblem due to the lack of non-perturbative methods to handle strong magneticfluctuations of itinerant electrons. We have non-pertubatively studiedthermodynamic properties and magnetic phase transitions of a two-dimensionalmulti-orbital Hubbard model exhibiting ferromagnetic ground states. QuantumMonte-Carlo simulations are employed, which are proved in a wide density regionfree of the sign problem usually suffered by simulations for fermions. BothHund's coupling and electron itinerancy are essential for establishing theferromagnetic coherence. No local magnetic moments exist in the system as apriori, nevertheless, the spin channel remains incoherent showing theCurie-Weiss type spin magnetic susceptibility down to very low temperatures atwhich the charge channel is already coherent exhibiting a weaklytemperature-dependent compressibility. For the SU(2) invariant systems, thespin susceptibility further grows exponentially as approaching zero temperaturein two dimensions. In the paramagnetic phase close to the Curie temperature,the momentum space Fermi distributions exhibit strong resemblance to those inthe fully polarized state. The long-range ferromagnetic ordering appears whenthe symmetry is reduced to the Ising class, and the Curie temperature isaccurately determined. These simulations provide helpful guidance to searchingfor novel ferromagnetic materials in both strongly correlated $d$-orbitaltransition metal oxide layers and the $p$-orbital ultra-cold atom opticallattice systems.