Role of conservation laws in the density matrix renormalization group

We explore matrix product state approximations to wave functions 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.

Automated summary

This article explores the use of matrix product state approximations for wave functions with spontaneously broken symmetries or criticality. Symmetries and their associated conservation laws result in block-sparse matrix product states, which offer faster numerical calculations and reduced memory requirements. However, in symmetry-broken and critical phases, the block-sparse ansatz leads to less accurate energy estimates. The article aims to characterize the role of conservation laws in matrix product states and determine the circumstances in which they are beneficial.