Quantum Matter

In this talk, I will focus on topological aspects and edge states of a spin system on a Kagome lattice. with the anisotropic XXZ and Dzyaloshinskii-Moriya interaction (DMI). I will begin with the rich phase diagram in the classical limit arising as a result of the interplay of the two interaction strengths, followed by a spin-wave analysis in some of these phases. These spin-waves (or magnons) are studied using the Holstein-Primakoff transformations.   In the  ferromagnetic phase in which all the spins point along the +z or -z direction the bulk bands are separated from each other by finite energy gaps. Finding the Chern numbers here one finds that, there are four topologically distinct phases sharing the same ground state spin-configuration.  Hence an infinite strip of the system hosts robust edge states which are directly related to the Chern number of the bands. The other phases also are found to have edge modes. However, these are not topologically protected because of the gapless nature of the energy dispersion. 

We uncover a rich phenomenology of the self-organized honeycomb network superstructure of one-dimensional metals in a nearly-commensurate charge-density wave 1T-TaS${}_2$, which may play a significant role in understanding global topology of phase diagrams and superconductivity. The key observation is that the emergent honeycomb network magically supports a cascade of flat bands, whose unusual stability we thoroughly investigate. Furthermore, by combining the weak-coupling mean-field and strong-coupling approaches, we argue that the superconductivity will be strongly enhanced in the network. This provides a natural cooperative mechanism of the charge order and superconductivity, which coexist side-by-side in the 1T-TaS${}_2$. Not only explaining the superconductivity, we show that abundant topological band structures including several symmetry-protected band crossings and corner states, which are closely related to that of the higher-order topology, appear. The results reported here can be generically applicable to various other systems with similar network superstructures.

Self-learning Monte Carlo (SLMC) method is a general-purpose numerical method to simulate many-body systems. SLMC can efficiently cure the critical slowing down in both bosonic and fermionic systems. Moreover, for fermionic systems, SLMC can generally reduce the computational complexity and speed up simulations even away from the critical points. For example, SLMC is more than 1000 times faster than the conventional method for the double exchange model in 8*8*8 cubic lattice. In addition, SLMC also provides a general framework to naturally integrate the advanced machine learning techniques into Monte Carlo. In this talk, I will give an introduction about the background, basic idea and the design principle of SLMC. Later, I will explicitly show how to use SLMC and its great accelerations in classic systems, free fermions coupled with classical spins systems, and interacting fermion systems. At the end, I will talk our recent developed a new type of neural network, which is motivated by the mean field theory and could be used to represent many physical Hamiltonians. We believe the new structural network would be highly efficient to identify different phases and accelerate the numerical simulations for even complex models.