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Journal of Magnetism and Magnetic Materials

Chiral entanglement landscapes: Insights from a four-spin interaction

S. Mahdavifar, F. Khastehdel Fumani, Mohammad Reza Soltani

Published Apr 24, 2026• 1 citation
Publisher
DOI
10.1016/j.jmmm.2026.174158

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Abstract In addition to flavor oscillations, Dirac neutrinos also undergo the so-called chiral oscillations, a consequence of the free-particle dynamics under the Dirac equation. Such a transition between different chiralities affect the flavor transitions, but also can generate non-trivial correlations between the internal degrees of freedom of the particle. In this paper, we show that the state of a massive oscillating neutrino produced by weak interaction process, is an hyperentangled state, in which flavor, chirality, and spin exhibit non-trivial correlations. Using complete complementarity relations, we show that both chiral and flavor oscillations redistribute correlations and coherence in time among different partitions of the system. In a similar way, we consider a spin entangled lepton-antineutrino pair and show that there is a dynamical redistribution of spin-spin entanglement into correlations and coherence between the other degrees-of-freedom. Our analysis provides a complete characterization of the quantum correlations involved in lepton-antineutrino pairs and in single particle neutrino evolution, and provides a further insight on possible routes to interpret and measure chiral oscillations.
We study the two-leg Heisenberg ladder with four-spin cyclic interaction using the (dynamical) density-matrix renormalization-group method. We demonstrate the dependence of the low-lying excitations in the spin wave, staggered dimer order, and scalar-chirality order structure factors on the four-spin cyclic interaction. We find that the cyclic interaction enhances spin-spin correlations with wave vector around momentum $({q}_{x},{q}_{y})=(\frac{\ensuremath{\pi}}{2},0)$. Also, the presence of long-range order in the staggered dimer and scalar-chirality phases is confirmed by a $\ensuremath{\delta}$-function peak contribution of the structure factors at energy $\ensuremath{\omega}=0$.
We have studied the phase diagram and entanglement of the one-dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization-group (QRG) approach to get the stable fixed points, critical point, and the scaling of coupling constants. This model has two phases: antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite-size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of spin operators which are defined by a nonlocal transformation.