Particle number conservation in quantum many-body simulations with matrix product operators

TL;DR

This paper explores how explicitly incorporating particle number conservation into matrix product operator simulations affects computational efficiency, revealing that global constraints can impose entanglement limits rather than speed gains.

Contribution

It extends the concept of conservation laws from matrix product states to matrix product operators, analyzing their impact on simulation efficiency and entanglement.

Findings

Conservation laws can impose entanglement constraints in MPO simulations.

Speed gains from symmetry sector restriction are not always realized.

Global particle number constraints can limit simulation performance.

Abstract

Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in simulation where the dynamically evolving entities are matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that in this case often the entanglement imposed by the global constraint of fixed particle number is the limiting factor.