The strange energy spectrum of approximate matrix product ground states

Steve White
University of California, Irvine (UCI)

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.

Presentation (PDF File)

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