Fermion bag approach to lattice field theories

We propose a new approach to the fermion sign problem in systems where there is a coupling U such that when it is infinite the fermions are paired into bosons, and there is no fermion permutation sign to worry about. We argue that as U becomes finite, fermions are liberated but are naturally confined to regions which we refer to as fermion bags. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three-dimensional massless lattice Thirring model as an example, we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find ν=0.87(2) and η=0.62(2). © 2010 The American Physical Society.

Lattice Engineering of III-Nitride Heterostructures and Their Applications

III-Nitride materials have recently become a promising candidate for superior applications over the current technologies. However, certain issues such as lack of native substrates, and high defect density have to be overcome for further development of III-Nitride technology. This work presents research on lattice engineering of III-Nitride materials, and the structural, optical, and electrical properties of its alloys, in order to approach the ideal material for various applications. We demonstrated the non-destructive and quantitative characterization of composition modulated nanostructure in InAlN thin films with X-ray diffraction. We found the development of the nanostructure depends on growth temperature, and the composition modulation has impacts on carrier recombination dynamics. We also showed that the controlled relaxation of a very thin AlN buffer (20 ~ 30 nm) or a graded composition InGaN buffer can significantly reduce the defect density of a subsequent epitaxial layer. Finally, we synthesized an InAlGaN thin films and a multi-quantum-well structure. Significant emission enhancement in the UVB range (280 – 320 nm) was observed compared to AlGaN thin films. The nature of the enhancement was investigated experimentally and numerically, suggesting carrier confinement in the In localization centers.