Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2007.01700 · Acta Physica Polonica A

Unsaturated Bipartite Entanglement of a Spin-1/2 Ising-Heisenberg Model on a Triangulated Husimi Lattice

Cesur Ekiz, Jozef Strečka

Published May 1, 2020• 6 citations
arXivHTMLPDF

Abstract

A bipartite entanglement between two nearest-neighbor Heisenberg spins of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is quantified using a concurrence.It is shown that the concurrence equals zero in a classical ferromagnetic and a quantum disordered phase, while it becomes sizable though unsaturated in a quantum ferromagnetic phase.A thermally-assisted re-entrance of the concurrence is found above a classical ferromagnetic phase, whereas a quantum ferromagnetic phase displays a striking cusp of the concurrence at a critical temperature.

DOI
10.12693/aphyspola.137.592

Related papers

Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices

Jozef Strečka, Cesur Ekiz

The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice.

arXiv:1503.01917•Physical Review E•May 26, 2015•19 citations

Magnetic properties and thermal entanglement on a triangulated Kagomé lattice

N.S. Ananikian, L. Ananikyan, Levon Chakhmakhchyan +1 more

The magnetic and entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Because of the separable character of Ising-type exchange interactions between the Heisenberg trimers the calculation of quantum entanglement in a self-consistent field can be performed for each of the trimers individually. The concurrence in terms of three qubit isotropic Heisenberg model in effective Ising field is non-zero even in the absence of a magnetic field. The magnetic and entanglement properties exhibit common (plateau and peak) features observable via (antferromagnetic) coupling constant and external magnetic field. The critical temperature for the phase transition and threshold temperature for concurrence coincide in the case of antiferromagnetic coupling between qubits. The existence of entangled and disentangled phases in saturated and frustrated phases is established.

arXiv:1012.5478•Journal of Physics A Mathematical and Theoretical•Dec 8, 2010•23 citations

A possible coexistence of spontaneous magnetic order and thermal entanglement in a spin-1/2 Ising–Heisenberg diamond-decorated square lattice

Azadeh Ghannadan, Jozef Strečka

The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice is exactly solved by the decoration-iteration transformation, which establishes an exact mapping correspondence with the spin-1/2 Ising model on a square lattice with an effective temperature-dependent interaction between the nearest-neighbor spins. Exact results for the pair correlation function and spontaneous magnetization of the Heisenberg spins gained from the exact mapping equivalence allow a straightforward implementation of the concurrence, which may serve as a measure of the bipartite entanglement within decorating Heisenberg spin pairs. It is evidenced that the concurrence gradually diminishes upon increase of temperature above a disordered monomer-dimer ground state until it completely vanishes at a threshold temperature, while the concurrence is either always zero above a spontaneously ordered ferrimagnetic ground state or it shows a peculiar thermally assisted reentrance accompanied with a mutual coexistence of the spontaneous ferrimagnetic long-range order and the thermal entanglement.

Chinese Journal of Physics•Jan 13, 2024•4 citations

Thermal Entanglement and Critical Behavior of Magnetic Properties on a Triangulated Kagomé Lattice

N.S. Ananikian, L. Ananikyan, Levon Chakhmakhchyan +1 more

The equilibrium magnetic and entanglement properties in a spin-1/2 Ising-Heisenberg model on a triangulated Kagomé lattice are analyzed by means of the effective field for the Gibbs-Bogoliubov inequality. The calculation is reduced to decoupled individual (clusters) trimers due to the separable character of the Ising-type exchange interactions between the Heisenberg trimers. The concurrence in terms of the three qubit isotropic Heisenberg model in the effective Ising field in the absence of a magnetic field is non-zero. The magnetic and entanglement properties exhibit common (plateau, peak) features driven by a magnetic field and (antiferromagnetic) exchange interaction. The (quantum) entangled and non-entangled phases can be exploited as a useful tool for signalling the quantum phase transitions and crossovers at finite temperatures. The critical temperature of order-disorder coincides with the threshold temperature of thermal entanglement.

Acta Polytechnica•Jan 2, 2011•0 citations

Chaotic spin-spin entanglement on a recursive lattice

Levon Chakhmakhchyan, S. Guérin, Claude Leroy

We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes.

arXiv:1504.04764•Physical Review E•Aug 3, 2015•1 citation

Interplay of Bipartite Entanglement between Two Geometrically Inequivalent Spin Pairs of a Spin-1/2 Heisenberg Distorted Tetrahedron

Katarína Karľová, Jozef Strečka

The energy spectrum, ground-state phase diagram, pair correlation functions, and concurrence are exactly calculated for a spin-1/2 quantum Heisenberg distorted tetrahedron in a magnetic field.The ground-state phase diagram in the interaction ratio versus magnetic field plane totally involves five different ground states, which differ from one another by the total spin, local pair correlation functions, and/or concurrence.In addition to the classical fully polarized ferromagnetic ground state there also appear four outstanding quantum ground states, two of which belong to a singlet sector and another two to a triplet sector.A degree of bipartite entanglement quantified through the concurrence is examined as a function of magnetic field, temperature, and the interaction ratio.

Acta Physica Polonica A•May 1, 2020•9 citations
A bipartite entanglement between two nearest-neighbor Heisenberg spins of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is quantified using a concurrence.It is shown that the concurrence equals zero in a classical ferromagnetic and a quantum disordered phase, while it becomes sizable though unsaturated in a quantum ferromagnetic phase.A thermally-assisted re-entrance of the concurrence is found above a classical ferromagnetic phase, whereas a quantum ferromagnetic phase displays a striking cusp of the concurrence at a critical temperature.
The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice.
The magnetic and entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Because of the separable character of Ising-type exchange interactions between the Heisenberg trimers the calculation of quantum entanglement in a self-consistent field can be performed for each of the trimers individually. The concurrence in terms of three qubit isotropic Heisenberg model in effective Ising field is non-zero even in the absence of a magnetic field. The magnetic and entanglement properties exhibit common (plateau and peak) features observable via (antferromagnetic) coupling constant and external magnetic field. The critical temperature for the phase transition and threshold temperature for concurrence coincide in the case of antiferromagnetic coupling between qubits. The existence of entangled and disentangled phases in saturated and frustrated phases is established.
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice is exactly solved by the decoration-iteration transformation, which establishes an exact mapping correspondence with the spin-1/2 Ising model on a square lattice with an effective temperature-dependent interaction between the nearest-neighbor spins. Exact results for the pair correlation function and spontaneous magnetization of the Heisenberg spins gained from the exact mapping equivalence allow a straightforward implementation of the concurrence, which may serve as a measure of the bipartite entanglement within decorating Heisenberg spin pairs. It is evidenced that the concurrence gradually diminishes upon increase of temperature above a disordered monomer-dimer ground state until it completely vanishes at a threshold temperature, while the concurrence is either always zero above a spontaneously ordered ferrimagnetic ground state or it shows a peculiar thermally assisted reentrance accompanied with a mutual coexistence of the spontaneous ferrimagnetic long-range order and the thermal entanglement.
The equilibrium magnetic and entanglement properties in a spin-1/2 Ising-Heisenberg model on a triangulated Kagomé lattice are analyzed by means of the effective field for the Gibbs-Bogoliubov inequality. The calculation is reduced to decoupled individual (clusters) trimers due to the separable character of the Ising-type exchange interactions between the Heisenberg trimers. The concurrence in terms of the three qubit isotropic Heisenberg model in the effective Ising field in the absence of a magnetic field is non-zero. The magnetic and entanglement properties exhibit common (plateau, peak) features driven by a magnetic field and (antiferromagnetic) exchange interaction. The (quantum) entangled and non-entangled phases can be exploited as a useful tool for signalling the quantum phase transitions and crossovers at finite temperatures. The critical temperature of order-disorder coincides with the threshold temperature of thermal entanglement.
We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes.
The energy spectrum, ground-state phase diagram, pair correlation functions, and concurrence are exactly calculated for a spin-1/2 quantum Heisenberg distorted tetrahedron in a magnetic field.The ground-state phase diagram in the interaction ratio versus magnetic field plane totally involves five different ground states, which differ from one another by the total spin, local pair correlation functions, and/or concurrence.In addition to the classical fully polarized ferromagnetic ground state there also appear four outstanding quantum ground states, two of which belong to a singlet sector and another two to a triplet sector.A degree of bipartite entanglement quantified through the concurrence is examined as a function of magnetic field, temperature, and the interaction ratio.