Abstract
The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin- Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.
Highlights
Quantum entanglement has been attracting a lot of attention in the last few years mainly due to its crucial role in the development of quantum computers, superdense coding, quantum communication, quantum teleportation, as well as quantum information theory [1,2,3]
The goals of the present paper are to shed a light on the nature of ground states invoked by the applied field, to identify the actual fractional plateaus in the zero-temperature magnetization process, to find out a general formula describing how the values of these plateaus depend on the current number of interconnected bipyramidal plaquettes and, to quantify the bipartite quantum entanglement between the Heisenberg spins in individual ground states
We will proceed to a discussion of the most interesting numerical results for the 2D spin-1/2 Ising–Heisenberg model in an external magnetic field with the antiferromagnetic Ising-type interaction J I < 0 between the Ising and Heisenberg spins
Summary
Quantum entanglement has been attracting a lot of attention in the last few years mainly due to its crucial role in the development of quantum computers, superdense coding, quantum communication, quantum teleportation, as well as quantum information theory [1,2,3]. The rigorous investigation of the bipartite entanglement in the pure Heisenberg models represents a complex task, which is considerably limited due to a noncommutability of spin operators in the Hamiltonian. This computational problem makes the rigorous study of the phenomenon in general inaccessible across whole parameter space of the systems. On the other hand, replacing some of the Heisenberg spins with three spin components by the Ising ones with only one (z-) component at the nodal lattice sites is the alternative way to exactly examine the entanglement in various simpler mixed-spin
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