Multipartite entanglement was thought to be intrinsically difficult to measure in solids, but recent work has established connections between multipartite entanglement, dynamic susceptibilities, and neutron scattering data, via the quantum Fisher information. This work focuses on the paradigmatic spin-half chain and shows that there are further simplifications: even static structure factors contain quantitative information about multipartite entanglement at low temperatures. Theory, numerics, and experiment then suggest that a high degree of multipartite entanglement is observable in Heisenberg chain compounds, including KCuF
3.
Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the Quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as
T→0. We argue that this implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale that is determined by universal properties, up to a non-universal amplitude. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. The 1D spin-
21 antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges non-trivially as
∼log(1/T)3/2. We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF
3, a material well-described by the Heisenberg chain.
Quantum systems subject to external monitoring manifest a rich phenomenology in their entanglement properties. Here, the authors use quantum Fisher information to uncover a multipartite entanglement phase transition in the monitored quantum Ising chain. By changing the measurement rate, they observe a shift from bounded to long-range multipartiteness of quantum correlations. They show that the quantum Fisher information displays distinct behavior from the entanglement entropy, and the two outline different phase boundaries.
Characterizing entanglement in quantum materials through experimentally accessible observables remains a central challenge. Quantum Fisher information associated with sums of one-site spin operators provides one route by linking entanglement to measurable magnetic response functions. Extending this approach to local composite observables requires new entanglement bounds. Here we establish a rigorous bound for the total nearest-neighbour vector chirality of periodic spin-
1/2 chains with an even number of sites. The quantum Fisher information per spin cannot exceed
k+1 for any
k-producible state, so exceeding this bound certifies entanglement depth of at least
k+1. Combining infinite density-matrix renormalization group and thermal pure quantum-state calculations, we demonstrate multipartite entanglement encoded in vector-chiral correlations at zero and finite temperatures in an extended
J1-
J2 XXZ chain. The spin-current coupling between vector chirality and electric polarization offers, in principle, access to this witness through dielectric loss spectroscopy in multiferroic magnets, extending entanglement diagnostics beyond dipolar spin correlations.
Abstract The theory of multipartite entanglement provides a robust framework for understanding complex phenomena in quantum many-body systems, while multipartite entanglement also serves as a key resource in numerous quantum information processing tasks. Using density matrix renormalization group calculations, we study the multipartite entanglement in one-dimensional quantum long-range ferromagnetic and antiferromagnetic Ising chains with algebraically decaying interactions 1/ r α , respectively. To quantitatively probe the system’s multipartite entanglement structure, we employ the quantum Fisher information (QFI). Our results reveal two key behaviors: as the system size increases, the QFI rises, while the multipartite entanglement density decreases and converges toward a constant value. The latter trend points to a fundamental constraint on entanglement distribution in the thermodynamic limit. We further discuss the effects of the magnetic field and the exponent α on the QFI. We find that the peak values of the QFI increase with increasing α . Additionally, the discontinuity in the QFI can be regarded as a powerful tool for characterizing quantum phase transitions in the systems.