Abstract
The spin-$\frac{1}{2}$ Ising-Heisenberg pentagonal chain is investigated with use of the star-triangle transformation, which establishes a rigorous mapping equivalence with the effective spin-$\frac{1}{2}$ Ising zigzag ladder. The investigated model has a rich ground-state phase diagram including two spectacular quantum antiferromagnetic ground states with a fourfold broken symmetry. It is demonstrated that these long-period quantum ground states arise due to a competition between the effective next-nearest-neighbor and nearest-neighbor interactions of the corresponding spin-$\frac{1}{2}$ Ising zigzag ladder. The concurrence is used to quantify the bipartite entanglement between the nearest-neighbor Heisenberg spin pairs, which are quantum-mechanically entangled in two quantum ground states with or without spontaneously broken symmetry. The pair correlation functions between the nearest-neighbor Heisenberg spins as well as the next-nearest-neighbor and nearest-neighbor Ising spins were investigated with the aim to bring insight into how a relevant short-range order manifests itself at low enough temperatures. It is shown that the specific heat displays temperature dependencies with either one or two separate round maxima.
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