Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

Abstract

Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about 5 atoms. One way to deal with this problem is to represent tensors using a tensor format. In this paper, we use CP format. Energy levels are computed by building a basis from vectors obtained by solving linear equations. The method can be thought of as a CP realization of a block inverse iteration method with multiple shifts. The CP rank of the tensors is fixed and the linear equations are solved with an Alternating Least Squares method. There is no need for rank reduction, no need for orthogonalization, and tensors with rank larger than the fixed rank used to solve the linear equations are never generated. The ideas are tested by computing vibrational energy levels of a 64-D bilinearly coupled model Hamiltonian and of acetonitrile(12-D).

References in corpus (3)

• The density-matrix renormalization group in the age of matrix product states
• Multilayer multi-configuration time-dependent Hartree method: implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine
• Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices

Cited by in corpus (4)

• Benchmarking vibrational spectra: 5000 accurate eigenstates of acetonitrile using tree tensor network states
• Trotter simulation of vibrational Hamiltonians on a quantum computer
• Computing excited eigenstates using inexact Lanczos methods and tree tensor network states
• Accurate, full-dimensional computations of thousands of complex vibrational eigenstates with tree tensor network states