Recorded 06 February 2024. Steve White of the University of California, Irvine, presents "The strange energy spectrum of approximate matrix product ground states" at IPAM's Tensor Networks Workshop. Abstract: Many methods for obtaining ground states are based on imaginary time evolution, where high energy components of an initial wavefunction are projected out. The approximate ground state one obtains after incomplete projection is a combination of low-lying states. The ground states from DMRG are different. They tend to have a large amplitude in the exact ground state and many small amplitude components at quite high energies. We discovered this in developing sampling methods for calculating the variance of the wavefunction, which can be used to extrapolate the energy to the infinite bond dimension limit. The perfect-sampled variance shows fat tails, which are not seen in most quantum Monte Carlo methods based on imaginary time evolution. We demonstrate an extrapolation technique based on a highly biased truncation of the variance sampling, which is not noisy and tends to the exact energy because the bias vanishes as the bond dimension increases. This extrapolation is very useful and practical in cases where traditional truncation error extrapolation is not available, such as single-site DMRG. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/tensor-networks/