Emergent quantum phases and topologies in electronic and spin systems

Abstract

The searching for and predicting novel phases and phenomena promotes the progress in the field of condensed matter physics. During the process, the importance of symmetry and topology has been continuously revealed and highlighted since a series of pioneering works. Nowadays, they have become the most powerful frameworks for our understanding of nature. In magnetic systems, topologically nontrivial states could emerge from interacting spins themselves or by coupling to other degrees of freedom such as electrons. Among them, the underlying symmetry and its interplay with the topology play important roles. This thesis is collection of our efforts to investigate the emergent quantum phases and topology in electronic and spin systems. From conventional SU(2) spins to more generic SU(N) spins, we present our study in two parts.

In the first part with SU(2) spins, we focus on the large-S limit where the behavior of spins is more like classical vectors and propose two distinct schemes to manipulate magnetic skyrmions. Such topological objects can be stabilized by the Dzyaloshinskii-Moriya interaction which requires the broken inversion symmetry. To this end, we first construct a Ginzburg-Landau theory and apply it to a multiferroic van der Waals heterostructure. Combining with ab initio calculations, we reveal that the multiferroicity serves as a bridge and can quantitatively transfer the inversion symmetry breaking to the magnetism and affect its topology. This mechanism provides an efficient channel to write and delete magnetic skyrmions via electric fields. For the other scheme we consider the interplay between classical spins and itinerant electrons by doping magnetic atoms on the surface of a three-dimensional topological insulator. Utilizing the same methods, we find that noncollinear spin textures, including the spin spirals and the skyrmion lattice, can be induced by Dirac electrons. Further studies on the feedback effect show that the behavior of Dirac electrons is drastically changed by the magnetic coupling.

In the other part, we go beyond the SU(2) spins by augmenting the symmetry group to SU(N). Quantum fluctuations would be strongly enhanced by this generalization but can still be harnessed in the large-N limit. We place the SU(N) spins in frustrated systems and search for the mean-field ground states strictly satisfying the local constraints. The frustration can come from different degrees of freedom, for example the lattice geometry and the interaction itself. These two situations correspond to antiferromagnetic Heisenberg models on a triangular lattice with the nearest-neighbor interaction and on a honeycomb lattice with both nearest-neighbor and next-nearest-neighbor interactions, respectively. Through a superior minimization algorithm with the self-consistency, a plethora of quantum states is identified, including but not limited to the critical Dirac spin liquid, topological chiral spin liquids, and various confined symmetry-breaking states. The rich phase diagram only reflects the tip of the iceberg. We hope our results can stimulate further studies on SU(N) physics, especially in the ultracold-atom system, and facilitate the understanding of the approximate models in solid state materials such as the twisted multilayer graphene.