Density Matrix Recursion Method: Genuine Multisite Entanglement Distinguishes Odd from Even Quantum Heisenberg Ladders

TL;DR

The paper presents an analytical recursive method to compute reduced density matrices in quantum spin ladders, revealing that genuine multipartite entanglement decreases with size in even-legged ladders but increases in odd-legged ones.

Contribution

It introduces the density matrix recursion method, enabling analysis of multipartite entanglement in complex quantum ladder systems, a novel approach in this context.

Findings

Genuine multipartite entanglement decreases with size in even-legged ladders.

Genuine multipartite entanglement increases with size in odd-legged ladders.

The method can generate reduced density matrices for various ladder configurations.

Abstract

We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices, with an arbitrary number of legs. The method can be used to calculate bipartite as well as multipartite physical properties, including bipartite and multi-partite entanglement. We apply this technique to distinguish between even- and odd-legged ladders. Specifically, we show that while genuine multi-partite entanglement decreases with increasing system size for the even-legged ladder states, it does the opposite for odd-legged ones.