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arXiv:1907.06027 · Physical review. B./Physical review. B

Nonclassicality of spin structures in condensed matter: An analysis of Sr14Cu24O41

Wen Yu Kon, Tanjung Krisnanda, Pinaki Sengupta, Tomasz Paterek

Published Dec 2, 2019• 7 citations
arXivHTMLPDF

Abstract

When two quantum systems are coupled via a mediator, their dynamics has traces of nonclassical properties of the mediator. We show how this observation can be effectively utilized to study the quantum nature of materials without well-established structure. A concrete example considered is ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. Measurements of low-temperature magnetic and thermal properties of this compound were explained with long-range coupling of unpaired spins through dimerized spin chains. We first show that the required coupling is not provided by the spin chain alone and give alternative compact two-dimensional spin arrangements compatible with the experimental results. Then we argue that any mediator between the unpaired spins must share with them quantum correlations in the form of quantum discord and, in many cases, quantum entanglement. In conclusion, present data witness quantum mediators between unpaired spins in ${\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$.

DOI
10.1103/physrevb.100.235103

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When two quantum systems are coupled via a mediator, their dynamics has traces of nonclassical properties of the mediator. We show how this observation can be effectively utilized to study the quantum nature of materials without well-established structure. A concrete example considered is Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​. Measurements of low-temperature magnetic and thermal properties of this compound were explained with long-range coupling of unpaired spins through dimerized spin chains. We first show that the required coupling is not provided by the spin chain alone and give alternative compact two-dimensional spin arrangements compatible with the experimental results. Then we argue that any mediator between the unpaired spins must share with them quantum correlations in the form of quantum discord and, in many cases, quantum entanglement. In conclusion, present data witness quantum mediators between unpaired spins in Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​.
Non-classical correlations arise in various quantum mechanical systems. Characterization and quantification of these correlations is an important and active branch of research in the field of quantum information theory. Investigation of non-classical correlations in condensed matter systems gives important insights about the characteristics of these systems. In particular, systems possessing a quantum critical point in their phase diagrams have attracted much attention due to the peculiar behavior of correlations near these points. In this thesis, we have investigated two distinct quantum spin models from the perspective of correlations and, we have discussed the correlation content of an important subclass of bipartite states. We start by an analytical calculation of the quantum discord for a system composed of spin-j and spin-1/2 subsystems possessing rotational symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in rotationally invariant states the amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have compared their quantum discord with entanglement and seen that quantum discord is higher than the entanglement. Next, we have investigated the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. We have demonstrated that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement. Finally, we have investigated various thermal quantum and total correlations in the anisotropic XY spin-chain with transverse magnetic field. We have shown that the ability of the considered measures to estimate the critical points of this system at finite temperature strongly depends on the anisotropy parameter of the Hamiltonian. Furthermore, we have studied the effect of temperature on long-range correlations of the XY chain.
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We have performed inelastic neutron scattering on a single crystal sample of Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ to study the spin dynamics of the Cu2O3{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}Cu2​O3​ spin ladder layers and CuO2{\mathrm{CuO}}_{2}CuO2​ chains. Our data are best fitted with a dispersion which has a spin gap of $32.5\ifmmode\pm\else\textpm\fi{}0.1\mathrm{meV}$ and a maximum of $193.5\ifmmode\pm\else\textpm\fi{}2.4\mathrm{meV}$, consistent with a coupling along the ladders, ${J}_{\ensuremath{\parallel}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}130\phantom{\rule{0ex}{0ex}}\mathrm{meV}$ and a rung coupling ${J}_{\ensuremath{\perp}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}72\mathrm{meV}$. Excitations with an energy transfer of approximately 11.5 meV arise from a dimer chain with an antiferromagnetic intradimer coupling J1=11.2meV{J}_{1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}11.2\mathrm{meV}J1​=11.2meV between next-nearest-neighbor Cu ions, and a ferromagnetic interdimer coupling ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1.1\mathrm{meV}$. The dimer chains have a periodicity of five units.
Quantum correlations are a fundamental property of quantum many-body states. Yet they remain experimentally elusive, hindering certification of genuine quantum behavior, especially in quantum materials. Here we show that the momentum-dependent dynamical susceptibility measured via inelastic neutron scattering enables the systematic reconstruction of a general family of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at arbitrary mutual distance. Using neutron scattering data on the compound KCuF3_33​ $\unicode{x2014}$ a system of weakly coupled S=1/2S=1/2S=1/2 Heisenberg chains $\unicode{x2014}$ and of numerically exact quantum Monte Carlo data, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed, they exhibit a new emergent length scale $\unicode{x2014}$ the quantum coherence length $\unicode{x2014}$ which is finite at any finite temperature (including when long-range magnetic order develops). Moreover, we show theoretically that coupled Heisenberg spin chains exhibit a form of quantum monogamy, with a trade-off between quantum correlations along and transverse to the spin chains. These results highlight real-space quantum correlators as an informative, model-independent means of probing the underlying quantum state of real quantum materials.
Spin models that have been proposed to describe dimerized chains, ladders, two-dimensional antiferromagnets, and other compounds are studied here when some spins are replaced by spinless vacancies, such as it occurs by Zn doping. A small percentage of vacancies rapidly destroys the spin gap, and their presence induces enhanced antiferromagnetic correlations near those vacancies. The study is performed with computational techniques which includes Lanczos, world-line Monte Carlo, and the density-matrix renormalization-group methods. Since the phenomenon of enhanced antiferromagnetism is found to occur in several models and cluster geometries, a common simple explanation for its presence may exist. It is argued that the resonating-valence-bond character of the spin correlations at short distances of a large variety of models is responsible for the presence of robust staggered spin correlations near vacancies and lattice edges. The phenomenon takes place regardless of the long distance properties of the ground state, and it is caused by a ``pruning'' of the available spin singlets in the vicinity of the vacancies. The effect produces a broadening of the low-temperature NMR signal for the compounds analyzed here. This broadening should be experimentally observable in the structurally dimerized chain systems $\mathrm{Cu}({\mathrm{NO}}_{3}{)}_{2}\ensuremath{\cdot}2.5{\mathrm{H}}_{2}\mathrm{O}$, CuWO4{\mathrm{CuWO}}_{4}CuWO4​, (VO)2P2O7(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}(VO)2​P2​O7​, and Sr14Cu24O41,{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41},Sr14​Cu24​O41​, in ladder materials such as SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​, in the spin-Peierls systems CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ and NaV2O5{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}NaV2​O5​, and in several others since it is a universal effect common to a wide variety of models and compounds. In addition, it is argued that the N\'eel order observed in SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​ upon Zn doping is induced by the local antiferromagnetic order discussed in this paper, enhanced by a favorable ratio between the actual Heisenberg couplings along chains and rungs, as reported in recent experimental literature. Based on this reasoning it is predicted here that other ladder materials such as Zn-doped Cu2(C5H12N2)2Cl4{\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}Cu2​(C5​H12​N2​)2​Cl4​ will not present N\'eel order at small Zn concentrations.
Entanglement has been extensively studied from the perspective of Quantum Information Processing for the last decade and various measures of entanglement, to quantify it are now available. Experimentally also it has been possible to measure entanglement in pure state, mostly in optics. However, in recent years there has been significant development in Quantum Condensed Matter systems, especially spin chains, where extraction of entanglement has been made possible through macroscopic witness operators like magnetic susceptibility. In this work, we have studied the magnetic properties of some spin chains, where the exchange interaction can be tuned by preparation technique and we have extracted a magnetic field and temperature dependence of entanglement from susceptibility and magnetization data taken at various temperatures and fields. The spin chains considered here fall in two categories, first one is an alternating dimer model and the second is an infinite spin chain. We have given the experimental plots of entanglement as a function of temperature and magnetic fields and compared them with the theoretical plots.