Dynamics of self-consistent wave function for fermionic Hubbard model

We have developed an efficient method for the dynamical simulation for the fermionic Hubbard model. An auxiliary vector field decoupling fermions is introduced at each site, and the self-consistent condition between the auxiliary fields and the non-interacting fermions is imposed for representing a physical state. The advantage of this approach relative to the conventional mean-field analysis is that the self-consistent wave function includes spatial fluctuations of the local order parameter and captures the critical phenomena of the thermodynamic phase transition. We have calculated the dynamical spin structure factor and demonstrated that it reproduces the exact result for a 4×4 lattice within a few percent error. We have studied the evolution of the magnon dispersion as a function of the interaction parameter for large systems, where the number of sites is of order 10³. We will present results for the dynamical response in equilibrium, as well as quench dynamics after changing the interaction parameter.

Reference: Gia-Wei Chern, Kipton Barros, Zhentao Wang, Hidemaro Suwa, and Cristian D Batista, "Semiclassical dynamics of spin density waves" arXiv:1708.08050