Analysis of Photo-Pumped Hubbard Model on a Square Lattice Using Randomized Singular Value Decomposition*

We investigate the dynamics of photo-excited states of the Hubbard model on a square lattice by decomposing the solution of the time-dependent Schrödinger equation into eigenmodes obtained by the randomized singular value decomposition (RSVD) [1]. Using the RSVD utilizing the dimensionality compression, we are able to decompose huge matrices that cannot be treated by conventional singular value decomposition. For a half-filled Hubbard model in the strong coupling limit on a square lattice, the optical absorption spectrum of the Hubbard model has been reproduced almost exactly by incorporating small number of eigenmodes obtained by RSVD. Encouraged by this success of RSVD, we take a 16-site Hubbard model away from half filling (12.5% hole doping) and perform mode decomposition of time-dependent wave functions after photo pumping. Calculating spin correlations for each mode, we find that some eigenmodes with energy close to Mott gap at half filling exhibit characteristic anisotropic correlations different from spin correlations in other energy regions.

[1] N. Halko, P. G. Martinsson, and J. A. Tropp, SIAM Review 2011 53:2, 217-288