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

TL;DR

This paper applies quantum singular value decomposition to the spin correlation matrix of a one-dimensional Heisenberg model, revealing insights into domain excitations and ground-state wavefunction structure.

Contribution

It introduces a quantum SVD approach to analyze the spin correlation matrix, connecting singular values to ground-state wavefunction weights and domain excitations.

Findings

Singular values scale with domain size.

Singular values relate to basis weights in the ground state.

Decomposition identifies relevant bases for the ground state.

Abstract

We present singular value decomposition of spin correlation matrix defined from the ground state of 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.