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Experimental implications of the entanglement transition in clustered quantum materials

Hannah R. Irons

Published Jul 1, 2016• 1 citation
OpenAlex

Abstract

Clustered quantum materials provide a new platform for the experimental study of many- body entanglement. Here we address a simple model featuring N interacting spins in a transverse field. The field can induce an entanglement transition (ET). We calculate the magnetisation, low-energy gap and neutron-scattering cross-section and find that the ET has distinct signatures, detectable at temperatures as high as 10% of the interaction strength. Unlike a quantum critical point, the signatures of the ET are stronger for smaller clusters.

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Clustered quantum materials provide a new platform for the experimental study of many- body entanglement. Here we address a simple model featuring N interacting spins in a transverse field. The field can induce an entanglement transition (ET). We calculate the magnetisation, low-energy gap and neutron-scattering cross-section and find that the ET has distinct signatures, detectable at temperatures as high as 10% of the interaction strength. Unlike a quantum critical point, the signatures of the ET are stronger for smaller clusters.
Quantum spin clusters provide a platform for the experimental study of many-body entanglement. Here we address a simple model of a single-molecule nanomagnet featuring NNN interacting spins in a transverse field. The field can control an entanglement transition (ET). We calculate the magnetization, low-energy gap, and neutron-scattering cross section and find that the ET has distinct signatures, detectable at temperatures as high as 5% of the interaction strength. The signatures are stronger for smaller clusters.
We show how the entanglement contained in states of spins arranged on a lattice may be lower bounded with observables arising in scattering experiments. We focus on the partial differential cross section obtained in neutron scattering from magnetic materials but our results are sufficiently general such that they may also be applied to, e.g., optical Bragg scattering from ultracold atoms in optical lattices or from ion chains. We discuss resonating valence bond states and ground and thermal states of experimentally relevant models---such as the Heisenberg, Majumdar-Ghosh, and XY models---in different geometries and with different spin numbers. As a by-product, we find that for the one-dimensional XY model in a transverse field such measurements reveal factorization and the quantum phase transition at zero temperature.
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
Entanglement between individual spins can be detected by using thermodynamics quantities as entanglement witnesses. This applies to collective spins also, provided that their internal degrees of freedom are frozen, as in the limit of weakly coupled nanomagnets. Here, we extend such approach to the detection of entanglement between subsystems of a spin cluster, beyond such weak-coupling limit. The resulting inequalities are violated in spin clusters with different geometries, thus allowing the detection of zero- and finite-temperature entanglement. Under relevant and experimentally verifiable conditions, all the required expectation values can be traced back to correlation functions of individual spins, which are now made selectively available by four-dimensional inelastic neutron scattering.
The dynamical structure factor of the transverse field Ising model (TFIM) shows universal power-law divergence at its quantum critical point, signatures of which have been arguably observed in inelastic neutron scattering studies of quantum spin chain materials, for example CoNb 2 O 6 . However, it has recently been suggested that its microscopic description is better captured in terms of a twisted Kitaev spin chain (TKSC) with bond-anisotropic couplings. Here, we present exact results for the dynamical structure factor of the TKSC across its quantum critical point, analyzing both the universal low-frequency response and the non-universal high-energy features. In addition, we explore extensions of the model including broken glide symmetry as well as the case of random, and incommensurate magnetic fields. Notably, in the latter case, the fermionic excitations exhibit a localization-delocalization transition, which is manifest in the dynamical response as a distinct signature at finite frequency. We discuss the relevance of these features for the observation of quantum critical response in experiments.
In this paper, we study three specific aspects of entanglement in small spin clusters. We first study the effect of inhomogeneous exchange coupling strengths on the entanglement properties of the S=12S=\frac{1}{2}S=21​ antiferromagnetic linear chain tetramer compound NaCuAsO4\mathrm{Na}\mathrm{Cu}\mathrm{As}{\mathrm{O}}_{4}NaCuAsO4​. The entanglement gap temperature TE{T}_{E}TE​ is found to have a nonmonotonic dependence on the value of $\ensuremath{\alpha}$, the exchange coupling inhomogeneity parameter. We next determine the variation of TE{T}_{E}TE​ as a function of SSS for a spin dimer, a trimer, and a tetrahedron. The temperature TE{T}_{E}TE​ is found to increase as a function of SSS but the scaled entanglement gap temperature tE{t}_{E}tE​ goes to zero as SSS becomes large. Last, we study a spin-1 dimer compound to illustrate the quantum complementarity relation. We show that in the experimentally realizable parameter region, magnetization and entanglement plateaus appear simultaneously at low temperatures as a function of the magnetic field. Also, the sharp increase in one quantity as a function of the magnetic field is accompanied by a sharp decrease in the other so that the quantum complementarity relation is not violated.