Density Matrix Renormalization Group in the Heisenberg Picture

TL;DR

This paper demonstrates that performing density matrix renormalization group calculations in the Heisenberg picture can significantly improve efficiency by focusing only on the observable of interest, sometimes achieving exact results with finite bond dimensions.

Contribution

It introduces a novel approach to DMRG in the Heisenberg picture, enhancing efficiency and accuracy over traditional methods by targeting specific observables.

Findings

Efficiency improvements in DMRG calculations in the Heisenberg picture

Potential for exact results with finite bond dimensions in certain cases

Reduction in computational resources by focusing on observables

Abstract

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some non-trivial cases, this approach can even be exact for finite bond dimensions.