Interaction effect in two-dimensional Dirac fermions

Based on the Dirac equations in the two-dimensional $\pi-$ flux model, we study the interaction effects both in nontrivial gapped and gapless Dirac equations with numerical exact diagonalization method. In the presence of the nearest and next nearest neighbor interactions: for nontrivial gapped Dirac equation, the topological phase is robust and persists in a finite region of the phase diagram; while for gapless Dirac equation, charge-density-wave and stripe phases are identified and the phase diagram in $(V_1, V_2)$ plane is obtained. When the next-next-nearest neighbor interaction is further included to gapless Dirac equation, the topological phase expected in the mean-field theory is absent. Our results are related to the possibility of dynamically generating topological phase from the electronic correlations.Comment: 7 pages, 8 figures. More discussins are added; accepted for publication in Physical Review

Dynamic Multi-Arm Bandit Game Based Multi-Agents Spectrum Sharing Strategy Design

For a wireless avionics communication system, a Multi-arm bandit game is mathematically formulated, which includes channel states, strategies, and rewards. The simple case includes only two agents sharing the spectrum which is fully studied in terms of maximizing the cumulative reward over a finite time horizon. An Upper Confidence Bound (UCB) algorithm is used to achieve the optimal solutions for the stochastic Multi-Arm Bandit (MAB) problem. Also, the MAB problem can also be solved from the Markov game framework perspective. Meanwhile, Thompson Sampling (TS) is also used as benchmark to evaluate the proposed approach performance. Numerical results are also provided regarding minimizing the expectation of the regret and choosing the best parameter for the upper confidence bound