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We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or $J_{1}$-$J_{2}$ Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behaviour of the entanglement entropy characterizing the unfrustrated Heisenberg chain as soon as $J_{2} >0.25$. This feature can be used as an indicator of the dimer phase transition that occurs at $J_{2} = J_{2}^{*} approx 0.2411 J_{1}$. Additionally, we also consider entanglement at the MG point $J_{2}=0.5 J_{1}$.
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We consider the application of the recursion method to the calculation of one-particle Greens functions for strongly correlated systems and propose a new way how to extract the information about the infinite system from the exact diagonalisation of small clusters. Comparing the results for several cluster sizes allows us to establish those Lanczos coefficients that are not affected by the finite size effects and provide the information about the Greens function of the macroscopic system. The analysis of this bulk-related subset of coefficients supplemented by alternative analytic approaches allows to infer their asymptotic behaviour and to propose an approximate analytical form for the terminator of the Greens function continued fraction expansion for the infinite system. As a result, the Greens function acquires the branch cut singularity corresponding to the incoherent part of the spectrum. The method is applied to the spectral function of one-hole in the Majumdar-Ghosh model (the one-dimensional $ t-J-J^{prime}$ model at $J^{prime}/J=1/2$). For this model, the branch cut starts at finite energy $omega_0$, but there is no upper bound of the spectrum, corresponding to a linear increase of the recursion coefficients. Further characteristics of the spectral function are band gaps in the middle of the band and bound states below $omega_0$ or within the gaps. The band gaps arise due to the period doubling of the unit cell and show up as characteristic oscillations of the recursion coefficients on top of the linear increase.
BaV3O8 contains both magnetic V4+(S=1/2) ions and non-magnetic V5+(S=0) ions. The V4+ ions are arranged in a coupled Majumdar-Ghosh chain like network. Our magnetic susceptibility chi(T) data fit well with the Curie-Weiss formula in the temperature range of 80-300K and it yields a Curie constant C=0.39cm3K/mole-V4+ and an antiferromagnetic Weiss temperature theta=-26K. The chi(T) curve shows a broad maximum at T~25K indicative of short-range order (SRO) and an anomaly corresponding to long-range order (LRO) at TN~6K. The value of the frustration index (f=mod[theta/TN]~5) suggests that the system is moderately frustrated. Above the LRO temperature the experimental magnetic susceptibility data match well with the coupled Majumdar-Ghosh chain model with the ratio of the nnn (next-nearest neighbor) to nn (nearest neighbor) magnetic coupling alpha=2 and Jnnn/kB=40K. In a mean-field approach when considering the inter-chain interactions, we obtain the total inter-chain coupling to be about 16K. The LRO anomaly at TN is also observe in the specific heat Cp(T) data and is not sensitive to an applied magnetic field up to 90kOe. A 51V NMR signal corresponding to the non-magnetic vanadium was observed. Anomalies at 6K were observed in the variation with temperature of the 51V NMR linewidth and in the spin-lattice relaxation rate 1/T1, indicating that they are sensitive to the LRO onset and fluctuations at the magnetic V sites. The existence of two components (one short and another long) is observed in the spin-spin relaxation rate 1/T2 data in the vicinity of TN. The shorter component seems to be intimately connected with the magnetically ordered state. We suggest that both magnetically ordered and non-long range ordered (non-LRO) regions coexist in this compound below the long range ordering temperature.
In this joint experimental and theoretical work magnetic properties of the Cu$^{2+}$ mineral szenicsite Cu$_3$(MoO$_4$)(OH)$_4$ are investigated. This compound features isolated triple chains in its crystal structure, where the central chain involves an edge-sharing geometry of the CuO$_4$ plaquettes, while the two side chains feature a corner-sharing zig-zag geometry. The magnetism of the side chains can be described in terms of antiferromagnetic dimers with a coupling larger than 200 K. The central chain was found to be a realization of the frustrated antiferromagnetic $J_1$-$J_2$ chain model with $J_1simeq 68$ K and a sizable second-neighbor coupling $J_2$. The central and side chains are nearly decoupled owing to interchain frustration. Therefore, the low-temperature behavior of szenicsite should be entirely determined by the physics of the central frustrated $J_1$-$J_2$ chain. Our heat-capacity measurements reveal an accumulation of entropy at low temperatures and suggest a proximity of the system to the Majumdar-Ghosh point of the antiferromagnetic $J_1$-$J_2$ spin chain, $J_2/J_1=0.5$.
In a recent paper (Commun. Phys. 3, 100) Znidaric studies the growth of higher Renyi entropies in diffusive systems and claims that they generically grow ballistically in time, except for spin-1/2 models in d=1 dimension. Here, we point out that the necessary conditions for sub-ballistic growth of Renyi entropies are in fact much more general, and apply to a large class of systems, including experimentally relevant ones in arbitrary dimension and with larger local Hilbert spaces.
We demonstrate how quantum entanglement can be directly witnessed in the quasi-1D Heisenberg antiferromagnet KCuF$_3$. We apply three entanglement witnesses --- one-tangle, two-tangle, and quantum Fisher information --- to its inelastic neutron spectrum, and compare with spectra simulated by finite-temperature density matrix renormalization group (DMRG) and classical Monte Carlo methods. We find that each witness provides direct access to entanglement. Of these, quantum Fisher information is the most robust experimentally, and indicates the presence of at least bipartite entanglement up to at least 50 K, corresponding to around 10% of the spinon zone-boundary energy. We apply quantum Fisher information to higher spin-S Heisenberg chains, and show theoretically that the witnessable entanglement gets suppressed to lower temperatures as the quantum number increases. Finally, we outline how these results can be applied to higher dimensional quantum materials to witness and quantify entanglement.
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