I have developed a variety of new AFQMC methods with my adviser Shiwei Zhang. These methods are: 1. Adding symmetry in both trial wave function and projector to AFQMC 2. Developing the release constraint method 3. Using force-bias method to improve the efficiency in Metropolis framework 4. Solving the infinite variance problem.
We used these new AFQMC methods to study the two-dimensional Hubbard model as a part of the Simons Foundation Many Electron Collaboration. Our results served as a benchmark to other numerical algorithms at half-filling, and provided highly accurate results away from half-filling. The benchmark study showed that the AFQMC is likely the most accurate general method for extended systems at present. A variety of other many-electron problems can now be tackled.
The Fermi gas with a zero-range attractive interaction has generated a great deal of research activities. The system is of interest in both condensed-matter and nuclear physics, and it can be realized in a laboratory with great precision and control, using ultracold atoms. We have done exact ground state simulations of this system. We obtained equation of state, contact parameter, condensation fraction, and pair wave functions. These results provide valuable benchmarks for future studies and allow precise comparisons with experiments. Our numerical results will also facilitate future local-density calculations in a variety of systems relevant to experiment, including thermodynamics and out of equilibrium properties in the presence of a trap.
When spin orbit coupling is added, the 2D Fermi gas becomes richer and more complex. We are currently studying the system with Rashba spin orbit coupling, by sampling the generalized Hartree-Fock wave function in QMC. We have detected several exotic phases, including a helical spin state, triplet pairing and spin nematic order.
We are also working on imaginary time correlations in AFQMC, which enable us to calculate dynamic information instead of static properties. Using that we can extract the gap for quantum systems, and calculate structure factors which can be directly compared with experiments. We are also attempting to marry AFQMC and Density Matrix Embedding Theory (DMET), where AFQMC is the impurity solver in DMET, allowing us to reach much larger system size.
I have worked on Exact Diagonalization for the topological phase transition in interacting Haldane model, and have some research experience in Dynamic Mean Field Theory, Continuous Time Quantum Monte Carlo and Density Matrix Renormalization Group.
You can find my publication list here.