Micromagnons and long-range entanglement in ferrimagnetic ground states

TL;DR

The paper addresses how quantum entanglement manifests in ferrimagnetic spin chains with alternating spins $s_1= frac{1}{2}$ and $s_2= frac{3}{2}$. It combines exact diagonalization and DMRG with a micromagnon ($\mu$-magnon) framework to express ground-state amplitudes in terms of a small set of Néel-structure configurations and separation-dependent corrections, enabling efficient truncations. The authors show that bipartite entanglement is confined to nearest neighbors, but genuine long-range multipartite entanglement persists between distant spin pairs, which is enhanced by open boundaries. Their truncation-and-dictionary approach reproduces reduced-state entanglement in larger systems in agreement with DMRG and provides a scalable path toward studying higher-dimensional ferrimagnetic lattices, with potential implications for quantum information in solid-state systems. The results offer a physically intuitive picture of ground-state correlations and demonstrate that a small, well-chosen set of configurations captures the essential entanglement structure, including long-range multipartite correlations.

Abstract

While significant attention has been devoted to studying entanglement in photonic systems, solid-state spin lattices remain relatively underexplored. Motivated by this gap, we investigate the entanglement structure of one-dimensional ferrimagnetic chains composed of alternating spin-1/2 and spin-3/2 particles. We characterize the ground-state correlations using exact diagonalization and the Density Matrix Renormalization Group method. Although the bipartite entanglement is restricted to nearest neighbors, we reveal the presence of long-range genuine multipartite entanglement between spatially separated spin pairs. These findings advance our understanding of quantum correlations in ferrimagnetic materials. The micromagnon description allows to provide fast approximation of ground states of ferrimagnets and emphasizes presence of multipartite correlations not widely discussed thus far.

Figures (9)

• Figure 1: Logarithms of moduli $\log|\alpha|$ of amplitudes of configurations in the ground state of 14-site mixed spin chain versus the classical energy of the configurations (left) and the number of spin-$\bm{\frac{3}{2}}$ changed with respect to the Néel sea (right). The coloring describes the number of $\mu$-magnons, i.e, the number of spins-$\frac{1}{2}$ changed with respect to the Néel sea.
• Figure 2: (a) Most typical spin structures identifiable in the ground state. Split $\mu$-magnons with larger separations are also possible. Magnetization $-\bm{\frac{3}{2}}$ is attained when three $\mu$-magnons, at least one of which is split, overlap, which is associated with a very low amplitude. (b) A graphical representation of a classical mechanism of a $\mu$-magnon creation. The Néel sea, not being a true ground-state, is a subject to fluctuations. Distortions from the Néel pattern require less additional energy, when they are close together. Quantum-mechanical energy minimization dictates the amplitudes between fluctuating and non-fluctuating components.
• Figure 3: (a) Amplitudes of various magnetic structures in the ground state of the Heisenberg Hamiltonian of a ring of alternating sites of $\frac{1}{2}$ and $\bm{\frac{3}{2}}$ spins. In this example we have set the internal Heisenberg coupling $J = 1$, and the external magnetic field $B= 0.1$. (b) Amplitudes for an alternating sites of spins $\frac{1}{2}$ and $\bm{1}$.
• Figure 4: Infidelity of a truncated reduced states of four consecutive sites in function of the fraction of included spin-$\left(\frac{1}{2},\mathbf{\frac{3}{2}}\right)$ configurations for $N=10$ (blue), 12 (orange) and 14 (green).
• Figure 5: (a) Four-partite negativity between two separated spin pairs in the ground state of a very-long closed chain of alternating spins $\frac{1}{2}$ - $\bm{\frac{3}{2}}$, $\frac{1}{2}$ - $\bm{1}$, and $\frac{1}{2}$ - $\frac{1}{2}$. The reduced density matrix of the four sites, two spin pairs, is denoted by $\rho_{abcd}$. For simplicity the first spin pair is chosen at the beginning of the chain: $(a,b) = (1,2)$. The second spin pair is separated by a distance $D$: (c,d) = $(3+D,4+D)$, as illustrated in the bottom panel (b). For this example we have set the internal Heisenberg coupling $J = 1$ and the external magnetic field $B= 0.1$.