Breakdown of intermediate one-half magnetization plateau of spin-1/2 Ising-Heisenberg and Heisenberg branched chains at triple and Kosterlitz-Thouless critical points

Abstract

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 DMRG 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.

Unconventional Thermal and Magnetic-Field-Driven Changes of a Bipartite Entanglement of a Mixed Spin-(1/2,S) Heisenberg Dimer with an Uniaxial Single-Ion Anisotropy

“…Due to length of explicit form of the Equation ( 25), the readers can find them in Appendix B. At the same time, the complete list of partially transposed density matrices ρT 1/2 for the mixed spin-(1/2,S) Heisenberg dimers with specific spin values S = 1, 3/2, 2, 5/2 is given in Appendix C. Analysing Equation (25) in detail one identifies that only eigenvalues λ − S z tm can be negative, and hence, the respective bipartite entanglement is in accordance to the definition (2) determined by the formula…”

“…From a theoretical perspective low-dimensional Heisenberg spin models seem to be a reasonable theoretical ground, which allows an exact study of the quantum and thermal entanglement depending on external stimuli such as the magnetic field and/or temperature [16][17][18][19][20][21][22][23][24][25][26][27][28]. Besides the most intensively analysed spin-1/2 case, a few theoretical works were focused on the entanglement of the mixed-spin Heisenberg systems .…”

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising–Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids

“…To date, the bipartite entanglement has been rigorously examined in several one- (1D) and two-dimensional (2D) mixed-spin Ising–Heisenberg models formed by the identical Heisenberg dimers or triangular clusters which interact with each other via the intermediate nodal Ising spin(s) [ 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]. The investigations brought a deeper insight into the thermal and magnetic-field-driven changes of the phenomenon [ 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ], the impact of the model’s parameters on the phenomenon [ 36 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ], as well as the evolution of the phenomenon near and above second-order (continuous) phase transitions [ 44 , 45 ] without any artefacts arising from approximations. Despite their simplicity and the general opinion that the simpler mixed-spin Ising–Heisenberg systems involving isolated local quantum correlations are artificial models, some of the results were in a very good correspondence with ones obtained for more complex Heisenberg counterparts [ 40 ] and also with experiments [ 38 , 46 , 47 ].…”

“…To date, the bipartite entanglement has been rigorously examined in several one-(1D) and two-dimensional (2D) mixed-spin Ising-Heisenberg models formed by the identical Heisenberg dimers or triangular clusters which interact with each other via the intermediate nodal Ising spin(s) [36][37][38][39][40][41][42][43][44][45]. The investigations brought a deeper insight into the thermal and magnetic-field-driven changes of the phenomenon [36][37][38][39][40][41][42][43], the impact of the model's parameters on the phenomenon [36,[39][40][41][42][43][44][45], as well as the evolution of the phenomenon near and above second-order (continuous) phase transitions [44,45] without any artefacts arising from approximations. Despite their simplicity and the general opinion that the simpler mixed-spin Ising-Heisenberg systems involving isolated local quantum correlations are artificial models, some of the results were in a very good correspondence with ones obtained for more complex Heisenberg counterparts [40] and also with experiments [38,46,47].…”

Ground State, Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising-Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids

“…The investigations brought a deeper insight into the thermal and magnetic-field-driven changes of the phenomenon [36][37][38][39][40][41][42][43], the impact of the model's parameters on the phenomenon [36,[39][40][41][42][43][44][45], as well as the evolution of the phenomenon near and above second-order (continuous) phase transitions [44,45] without any artefacts arising from approximations. Despite their simplicity and the general opinion that the simpler mixed-spin Ising-Heisenberg systems involving isolated local quantum correlations are artificial models, some of the results were in a very good correspondence with ones obtained for more complex Heisenberg counterparts [40] and also with experiments [38,46,47].…”