Abstract:
There are many degenerate ground states in the geometrically frustrated spin systems, which can produce novel states. I will introduce an extremely frustrated lattice-Triangular Kagome Lattice (TKL). We obtain the exact solutions for the Ising model, Quantum+Ising model, and Dimer model on the TKL. The rich phase diagrams are found. Especially a topological phase - Kagome loop gas is found in the Quantum+Ising model on the TKL. The residual zero-temperature entropies for the most frustrated cases on the TKL are found to be ln72=4.2767 for the Ising model and 2.5258 for the Quantum+Ising model respectively. By using the cellular dynamical mean-field theory, we obtain the rich phase diagrams in the Hubbard model on the TKL. A short rang resonating valence-bond spin liquid phase is claimed. In the second part, I will talk about the dynamics of two initially correlated qubits coupled to their own separate spin baths modeled by a XY spin chain. We find the analytical expression of the quantum discord for the system. A sudden transition is found to exist between classical and quantum decoherence by choosing certain initial states. We find that the sudden transition happens near the critical point, which provides a new way to characterize the quantum phase transition. Furthermore, we propose a scheme to prolong the transition time of the quantum discord by applying the bang-bang pulses.