Abstract
The Kondo lattice model is one of the most fundamental models that have received tremendous theoretical interest. It describes strongly correlated systems with interaction between itinerant electrons and local magnetic moments. This interaction plays an important role in heavy fermion materials, where local magnetic moments interact with 4f or 5f electrons which behaves as if they are effectively much heavier than themselves. In this thesis, we present a few numerical studies on the Kondo lattice model and models based on Kondo chains.
Tensor network is a geometric architecture composed of connected tensors to represent quantum many body states. The representation turns out to be surprisingly efficient for area law states, in which the entanglement entropy scales linearly with the surface area of the system, rather than the volume as in a generic state. Tensor network algorithms have witnessed fast development in the past near 30 years. Density matrix renormalization group (DMRG), popularized in the last two decades for low dimensional system studies, and time-evolving block decimation (TEBD) are two representatives. In this thesis, we characterize the phases of one-dimensional Kondo lattice model with quantum localized spins using DMRG, and present the quench dynamics of the model using TEBD.
Highly frustrated magnets have attracted considerable attention with its intriguing and sometimes unexpected magnetic phases. In this thesis, we present an extensive numerical study of a new type of frustrated itinerant magnetism on the pyrochlore lattice. In this theory, the pyrochlore magnet can be viewed as a cross-linking network of Kondo or double-exchange chains. Contrary to models based on Mott insulators, this itinerant magnetism approach provides a natural explanation for several spin and orbital superstructures observed on the pyrochlore lattice. Through extensive Monte Carlo simulations, we obtain the phase diagrams at two representative electron filling fractions n = 1/2 and 2/3. For the half filling case, we observed a paramagnetic phase and an all-in-all-out phase, mimicking a spin ice. For the case of 2/3 filling, we found a (1/3, 1/3, 1) magnetic order, ferromagnetic phase, paramagnetic phase and an unexpected (1/2, 1/2, 1/2) order. In particular, we show that the intriguing glassy magnetic state characterized by ordering wavevectors q = (1/3, 1/3, 1) gives a rather satisfactory description of the low temperature phase recently observed in spinel GeFe$_2$O$_4$.
Finally, we present extensive large-scale dynamical simulations of the phase separated states, which are a mixture of ferromagnetic metallic cluster and antiferromagnetic insulating regions, in the double exchange model. These inhomogeneous electronic states play a crucial role in the colossal magnetoresistance phenomenon (CMR). The double-exchange model (Kondo lattice model) is considered as a major mechanism for its electronic phase separation. We present an innovative and efficient von-Neumann Landau-Lifshitz dynamics framework which enables large-scale dynamical simulation of inhomogeneous electronic states for the very first time. We compute the dynamical structure factor of these nanoscale textures using. Dynamical signatures of the various underlying magnetic structures are identified. At small hole doping, the structure factor exhibits a dominating signal of magnons from the background N\'eel order and localized modes from magnetic polarons. A low-energy continuum due to large-size ferromagnetic clusters emerges at higher doping levels. Implications for experiments on magnetoresistive manganites are also discussed.
