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arXiv:2504.18724 · Physical review. B./Physical review. B

Micromagnons and long-range entanglement in ferrimagnetic ground states

Marcin Wieśniak, Ankit Kumar, Idriss Hank Nkouatchoua Ngueya

Published Sep 29, 2025• 0 citations
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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.

DOI
10.1103/wwr6-l3dq

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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.
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S1>S2,{S}_{1}>{S}_{2},S1​>S2​, using 1/S1/S1/S spin-wave expansions, density-matrix renormalization group, and exact diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate-incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.
We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.
We provide insight into the quantum correlations structure present in strongly correlated systems beyond the standard framework of bipartite entanglement. To this aim we first exploit rotationally invariant states as a test bed to detect genuine tripartite entanglement beyond the nearest neighbor in spin-1/2 models. Then we construct in a closed analytical form a family of entanglement witnesses which provides a sufficient condition to determine if a state of a many-body system formed by an arbitrary number of spin-1/2 particles possesses genuine tripartite entanglement, independently of the details of the model. We illustrate our method by analyzing in detail the anisotropic XXZXXZXXZ spin chain close to its phase transitions, where we demonstrate the presence of long-range multipartite entanglement near the critical point and the breaking of the symmetries associated with the quantum phase transition.
Ferrimagnets are antiparallel-ordered magnetic states in a bipartite lattice with two alternating unequal spins, which exhibit both ferromagnetic and antiferromagnetic properties. Several theoretical studies have explored the magnetic properties of ferrimagnets, but the entanglement entropy of ferrimagnets with arbitrary spin combinations has not been studied. In this study, we analytically derive the intersublattice entanglement entropy of a ferrimagnetic spin chain using the method that has been applied to the antiferromagnetic case. The analytical results are numerically verified using the density-matrix renormalization group. Going beyond the results for antiferromagnets, the entanglement entropy of ferrimagnets for fixed anisotropy is shown to solely depend on the difference of spins relative to its geometric average, and the quantity is shown to be stable against small-parameter variations.
Ground-state properties of ferrimagnetic XXZ chains with alternating spins S A and S B with nearest-neighbor exchange interaction are discussed based upon the results for finite-size systems obtained mainly by the exact diagonalization method and partly by the density matrix renormalization group method. For -1<Δ<1, where Δ is the parameter of anisotropy of the interactions, the ground state is unique or doubly degenerate and gapless. When Δ=1, the ground state of 2 N sites is the state with total spin N | S A - S B |, and has nonvanishing Néel long-range order parameter. For Δ>1, the ground state is doubly degenerate Néel long-range ordered state with a finite energy gap.
We study ground-state properties of the Heisenberg frustrated spin chain with interactions up to fourth nearest neighbors by the exact-diagonalization method and the density matrix renormalization group method. We find that ferrimagnetism is realized not only in the case of S=1/2 but also S=1 despite that there is only a single spin site in each unit cell determined from the shape of the Hamiltonian. Our numerical results suggest that a "multi-sublattice structure" is not required for the occurrence of ferrimagnetism in quantum spin systems with isotropic interactions.