Role of conservation laws in the Density Matrix Renormalization Group

TL;DR

This paper investigates how conservation laws influence the efficiency and accuracy of matrix product state approximations in quantum systems, especially in symmetry-broken and critical phases.

Contribution

It characterizes the role of conservation laws in matrix product states and identifies when exploiting symmetries improves or hinders accuracy.

Findings

Symmetries lead to faster computations and lower memory usage.

In symmetry-broken and critical phases, symmetry-based ansatzes may be less accurate.

The paper determines conditions under which conservation laws are beneficial.

Abstract

We explore matrix product state approximations to wavefunctions which have spontaneously broken symmetries or are critical. We are motivated by the fact that symmetries, and their associated conservation laws, lead to block-sparse matrix product states. Numerical calculations which take advantage of these symmetries run faster and require less memory. However, in symmetry-broken and critical phases the block sparse ansatz yields less accurate energies. We characterize the role of conservation laws in matrix product states and determine when it is beneficial to make use of them.