Quantum Singular Value Decomposition of Spin Correlation Matrix in One-Dimensional Heisenberg Model

We present singular value decomposition of the spin correlation matrix defined from the ground state of the one-dimensional antiferromagnetic quantum Heisenberg model. The decomposition creates a data set that coincides with various domain excitations from classical antiferromagnetic state. We determine the scaling relation for the singular values as a function of the domain size. The singular values are closely related to the square of weights of the bases in the ground-state wavefunction. The nature of the singular value decomposition is to precisely estimate the appropriate bases and corresponding weights of the ground-state wavefunction.

Automated summary

This study focuses on the singular value decomposition of the spin correlation matrix from the ground state of the one-dimensional antiferromagnetic quantum Heisenberg model. By determining the scaling relation for the singular values as a function of domain size, it was found that the singular values are closely linked to the square of weights of the bases in the ground-state wavefunction, allowing for a precise estimation of the appropriate bases and corresponding weights of the ground-state wavefunction.