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Physical review. B./Physical review. B

Exact and density matrix renormalization group studies of two mixed spin- (12,52,12) branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

Fabiana Souza, Luan M. Veríssimo, Jozef Strečka, M. L. Lyra, Maria S. S. Pereira

Published Aug 17, 2020• 26 citations
Publisher

Abstract

The mixed-spin Ising-Heisenberg and Heisenberg branched chains whose magnetic backbone consists of regularly alternating spins 1/2 and 5/2, the latter of which are additionally coupled to an extra spin 1/2 providing lateral branching, are investigated using exact analytical and density matrix renormalization group (DMRG) methods. The proposed spin-chain models capture some relevant aspects of the heterotrimetallic coordination polymer $[\mathrm{Cu}\mathrm{Mn}(\mathrm{L})][\mathrm{Fe}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{Cl}{\mathrm{O}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$. The mixed spin-$(1/2,5/2,1/2)$ Ising-Heisenberg branched chain is exactly solvable under the assumption of an Ising-like exchange coupling along the chain, while the lateral branching is treated as an anisotropic $XXZ$ Heisenberg exchange interaction. We determine the ground-state phase diagram and quantify a bipartite quantum entanglement between dimers at lateral branching. It is shown that the studied mixed-spin Ising-Heisenberg branched chain accurately fits available experimental data for temperature dependence of the magnetic susceptibility. The ground-state phase diagram of the analogous mixed spin-$(1/2,5/2,1/2)$ Heisenberg branched chain is obtained within the DMRG method. The ground-state phase diagrams of the Ising-Heisenberg and its full Heisenberg counterpart are contrasted. In particular, the ground-state phase diagram of the mixed-spin Heisenberg branched chain involves a special Gaussian critical point, for which a proper finite-size scaling analysis is provided to accurately estimate its location and the correlation length critical exponent.

DOI
10.1103/physrevb.102.064414

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Density-matrix renormalization group calculations are used to determine the ground-state phase diagram of the mixed spin-(1/2, 5/2, 1/2) Heisenberg chain whose backbone consists of regularly alternating s=1/2s=1/2s=1/2 and S=5/2S=5/2S=5/2 spins, the latter of which are coupled to additional s=1/2s=1/2s=1/2 spins providing lateral branching. The proposed magnetic structure aims to describe the main characteristics of the heterotrimetallic coordination polymer $[{\mathrm{Cu}}^{\mathrm{II}}{\mathrm{Mn}}^{\mathrm{II}}({\mathrm{L}}^{1})][{\mathrm{Fe}}^{\mathrm{III}}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\phantom{\rule{4pt}{0ex}}\ifmmode\cdot\else\textperiodcentered\fi{}\phantom{\rule{4pt}{0ex}}{\mathrm{ClO}}_{4}\phantom{\rule{4pt}{0ex}}\ifmmode\cdot\else\textperiodcentered\fi{}\phantom{\rule{4pt}{0ex}}{\mathrm{H}}_{2}\mathrm{O}$. The full ground-state phase diagram in the parameter space exchange anisotropy versus magnetic field unveils special critical points, at which the intermediate magnetization plateaus emergent at 3/7 and 5/7 of the saturation magnetization vanish. A detailed description of the zero-temperature magnetization process and pair entanglement entropy is accomplished with the aim to distinguish the main coupling regimes. A scaling analysis is performed to accurately locate Kosterlitz-Thouless and Gaussian critical points. In particular, we introduce a new finite-size scaling protocol to properly extract the critical parameters from the size dependence of the magnetic-field range corresponding to the magnetization plateau in the close vicinity of the Gaussian point at which two gapped phases meet.
The spin-1/2 Ising-Heisenberg branched chain composed of regularly alternating Ising spins and Heisenberg dimers involving an additional side branching is rigorously solved in a magnetic field by the transfer-matrix approach. The ground-state phase diagram, the magnetization process and the concurrence measuring a degree of bipartite entanglement within the Heisenberg dimers are examined in detail. Three different ground states were found depending on a mutual interplay between the magnetic field and two different coupling constants: the modulated quantum antiferromagnetic phase, the quantum ferrimagnetic phase, and the classical ferromagnetic phase. Two former quantum ground states are manifested in zero-temperature magnetization curves as intermediate plateaus at zero and one-half of the saturation magnetization, whereas the one-half plateau disappears at a triple point induced by a strong-enough ferromagnetic Ising coupling. The ground-state phase diagram and zero-temperature magnetization curves of the analogous spin-1/2 Heisenberg branched chain were investigated using density-matrix renormalization group calculations. The latter fully quantum Heisenberg model involves, besides two gapful phases manifested as zero and one-half magnetization plateaus, gapless quantum spin-liquid phase. The intermediate one-half plateau of the spin-1/2 Heisenberg branched chain vanishes at Kosterlitz-Thouless quantum critical point between gapful and gapless quantum ground states unlike the triple point of the spin-1/2 Ising-Heisenberg branched chain.
We investigate the teleportation of an entangled state via a couple of quantum channels, which are composed of a spin-1/2 Heisenberg dimer in two infinite Ising–Heisenberg chains. The heterotrimetallic coordination polymer CuIIMnII(L1)][FeIII(bpb)(CN)2]·ClO4 · H2O (abbreviated as Fe–Mn–Cu) can be regarded as an actual material for this chain. We apply the transfer-matrix approach to obtain the density operator for the Heisenberg dimer and use the standard teleportation protocol to derive the analytical expression of the density matrix of the output state and the average fidelity of the entanglement teleportation. We study the effects of the temperature T, anisotropy coupling parameter Δ, Heisenberg coupling parameter J 2 and external magnetic field h on the quantum channels. The results show that anisotropy coupling Δ and Heisenberg coupling J 2 can favor the generation of the output concurrence and expand the scope of the successful average fidelity.
Abstract The spin-1/2 Heisenberg branched chain with the unit cell composed of three spins in the main backbone and one spin at a side branching of one-dimensional chain is investigated with the help of density-matrix renormalization group (DMRG) and quantum Monte Carlo (QMC) methods. The DMRG simulations were employed to calculate zero-temperature magnetization curves and to construct the ground-state phase diagram, which is composed from four different ground states classified as gapped zero-plateau and one-half plateau phase, a gapless spin-liquid phase and a fully saturated phase. It is shown that the one-half magnetization plateau vanishes at the Kosterlitz–Thouless quantum critical point, which is wedged into a parameter space of the gapless quantum spin-liquid phase. The bipartite quantum entanglement between four distinct nearest-neighbor pairs of the spin-1/2 Heisenberg branched chain is quantified through the concurrence. It is found that the concurrence varies continuously within the quantum spin-liquid phase, where it may display a continuous rise, a continuous fall or eventually an intriguing rise-and-fall behavior. On the contrary, the concurrence is kept constant within two gapful zero- and one-half plateau phases. Temperature and magnetic-field dependencies of the magnetization and magnetic susceptibility computed within the QMC method uncover clear signatures of the quantum critical point at finite temperatures.
The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.
The spin-1/2 Ising-Heisenberg branched chain, inspired by the magnetic structure of three isostructural polymeric coordination compounds [(Tp)2Fe2(CN)6X (bdmap)Cu2(H2O)] ⋅ H2O to be further denoted as Fe2Cu2 (Tp = tris(pyrazolyl)hydroborate, bdmapH = 1,3-bis(dimethylamino)-2-propanol, HX = acetic acid, propionic acid or trifluoroacetic acid), is rigorously studied using the transfer-matrix method. The overall ground-state phase diagram reveals three distinct phases: a quantum antiferromagnetic phase, a quantum ferrimagnetic phase and a classical ferromagnetic phase. In the zero-temperature magnetization curve, two quantum ground states are manifested as intermediate plateaus at zero and half of the saturation magnetization, while the magnetization reaches its saturated value within the classical ferromagnetic phase. The bipartite entanglement between nearest-neighbor Heisenberg spins is more pronounced in the quantum ferrimagnetic phase compared to the quantum antiferromagnetic phase due to a fully polarized nature of the Ising spins. A reasonable agreement between theoretical predictions for the spin-1/2 Ising-Heisenberg branched chain and experimental data measured for a temperature dependence of the magnetic susceptibility and a low-temperature magnetization curve suggests strong antiferromagnetic coupling between nearest-neighbor Cu2+-Cu2+ magnetic ions and moderately strong ferromagnetic coupling between nearest-neighbor Cu2+-Fe3+ magnetic ions in the polymeric compounds Fe2Cu2. A thermal entanglement between nearest-neighbor Cu2+-Cu2+ magnetic ions persists up to a relatively high threshold temperature T ≈ 224 K and undergoes a transient magnetic-field-driven strengthening.