Scale-renormalized matrix-product states for correlated quantum systems

TL;DR

This paper introduces scale-renormalized matrix-product states (SR-MPS), a novel approach for efficiently modeling interacting quantum systems in higher dimensions, demonstrating faster convergence than traditional methods.

Contribution

The paper presents SR-MPS, a new generalization of MPS that incorporates scale renormalization for better performance in 2D and 3D quantum systems.

Findings

SR-MPS converge faster with matrix size than standard MPS

Lattice-symmetries significantly improve convergence speed

Effective for 2D transverse-field Ising model

Abstract

A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining of the lattice in which the blocks at each level are associated with matrix products that are further transformed (scale renormalized) with other matrices before they are assembled to form blocks at the next level. Using variational Monte Carlo simulations of the two-dimensional transverse-field Ising model as a test, it is shown that the SR-MPS converge much more rapidly with the matrix size than a standard MPS. It is also shown that the use of lattice-symmetries speeds up the convergence very significantly.