Frustration phenomenon in the spin-1/2 Ising–Heisenberg planar model of inter-connected trigonal bipyramid structures

Abstract

Ground-state and finite-temperature properties of the exactly solvable mixed spin-1/2 Ising-Heisenberg planar model composed of identical trigonal bipyramids that are arranged into a regular archimedean lattice are examined with the aim to clarify the frustration phenomenon at zero and finite temperatures. It is shown that the ground-state spin frustration persists even far above the second-order phase transition. If the interaction ratio between the Heisenberg and Ising exchange interactions is close enough to the ground-state boundaries between the neighboring phases, a remarkable re-entrance of the (non-)frustrated spin arrangement of the Heisenberg spins can be observed around the critical temperature of the model. It is also evidenced that entropy and specific heat show pronounced temperature variations not only around the critical temperature, but also in low-temperature regime if values of the interaction parameters are taken from neighborhood of the ground-state phase transitions, where energies of the neighboring phases are very close.

Bipartite entanglement in the spin-1/2 Ising-Heisenberg planar lattice constituted of identical trigonal bipyramidal plaquettes

“…The essence of this algebraic method is to substitute all decorating composite spins and associated interactions by effective Ising-type couplings between remaining nodal spins. Particular computational steps including the explicit formula for the effective Boltzmann's weight are listed in our recent paper [24]. 1 The result is the following rigorous mapping equivalence between the partition function Z of the spin-1/2 Ising-Heisenberg model and the one Z I of the uniform spin-1/2 Ising square lattice with the temperaturedependent effective nearest-neighbour coupling J e f f :…”

“…In view of the above facts, the goal of the present Letter is to explore a bipartite ground-state and thermal quantum entanglement in the recently proposed and exactly solved spin-1/2 Ising-Heisenberg model on a regular 2D lattice consisting of identical trigonal bipyramidal plaquettes in a zero magnetic field [24]. The outline is as follows.…”

Unconventional spin frustration due to two competing ferromagnetic interactions of a spin-1/2 Ising-Heisenberg model on martini and martini-diced lattice

“…The first exactly solved 2D spin-1/2 Ising-Heisenberg model on a doubly decorated square lattice displays for instance either a classical ferromagnetic or a quantum antiferromagnetic long-range order at sufficiently low temperatures, whereby the quantum antiferromagnetic ordering peculiarly comes from two competing ferromagnetic interactions [9]. The competition between the Ising and Heisenberg interactions might be also at origin of a more complex critical behavior including reentrant phase transitions [18][19][20][21] or even weakuniversal criticality [22]. It is worth mentioning, moreover, that a spontaneous long-range order may absent in 2D Ising-Heisenberg models being subject to a geometric spin frustration though the relevant residual entropy is generally lower in comparison with the Ising counterparts due to local quantum fluctuations [10][11][12].…”

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

“…In the present paper, we will rigorously solve a spin- Ising–Heisenberg model in a longitudinal magnetic field on 2D lattices formed by identical corner-sharing trigonal bipyramidal plaquettes. Our recent studies [ 45 , 48 ] of the model without magnetic field on the particular lattice with four inter-connected bipyramidal units have shown that this quantum mixed-spin model represents a suitable playground for a rigorous study of various unconventional physical phenomena such as the macroscopic degeneracy of the spontaneous long-range order caused by chiral spin degrees of freedom, the spin frustration, and the bipartite entanglement. The aforementioned findings motivated us to extend the investigation of the model also to the effect of the longitudinal magnetic field.…”