Partial Multipartite Entanglement in the Matrix Product State Formalism

TL;DR

This paper introduces a method to analyze partial multipartite entanglement within the matrix product state framework, maintaining the computational efficiency of the DMRG algorithm and revealing links between ground state properties and partial separability.

Contribution

The authors extend the MPS formalism to partially separable states, enabling efficient analysis of entanglement in solid state systems with the same effort as standard DMRG.

Findings

Method applies to typical condensed matter systems.

Polymerisation properties relate to partial separability.

Efficient analysis without increased computational cost.

Abstract

We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix renormalisation group (DMRG) algorithm. Consequently, it is applicable to all usually considered condensed matter systems where the DMRG algorithm is successful. We also show in exemplary cases, that polymerisation properties of ground states are closely connected to properties of partial separability, even if the ground state itself is not partially separable.