Explore a 51-minute lecture on the unique energy spectrum characteristics of approximate matrix product ground states presented by Steve White from the University of California, Irvine. Delve into the differences between ground states obtained through imaginary time evolution methods and those from Density Matrix Renormalization Group (DMRG) techniques. Discover how DMRG ground states exhibit large amplitudes in the exact ground state alongside small amplitude components at high energies. Examine the development of sampling methods for calculating wavefunction variance and their application in extrapolating energy to the infinite bond dimension limit. Learn about the fat-tailed distribution observed in perfect-sampled variance and its absence in most quantum Monte Carlo methods. Understand a novel extrapolation technique based on biased truncation of variance sampling, which proves valuable in scenarios where traditional truncation error extrapolation is not feasible, such as single-site DMRG. Read more