14 research outputs found
Arnold Tongues and Feigenbaum Exponents of the Rational Mapping for Q-state Potts Model on Recursive Lattice: Q<2
We considered Q-state Potts model on Bethe lattice in presence of external
magnetic field for Q<2 by means of recursion relation technique. This allows to
study the phase transition mechanism in terms of the obtained one dimensional
rational mapping. The convergence of Feigenabaum and
exponents for the aforementioned mapping is investigated for the period
doubling and three cyclic window. We regarded the Lyapunov exponent as an order
parameter for the characterization of the model and discussed its dependence on
temperature and magnetic field. Arnold tongues analogs with winding numbers
w=1/2, w=2/4 and w=1/3 (in the three cyclic window) are constructed for Q<2.
The critical temperatures of the model are discussed and their dependence on Q
is investigated. We also proposed an approximate method for constructing Arnold
tongues via Feigenbaum exponent.Comment: 15 pages, 12 figure
Magnetic Properties and Thermal Entanglement on a Triangulated Kagome 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.Comment: 21 pages, 13 figure
Thermal Entanglement of a Spin-1/2 Ising-Heisenberg Model on a Symmetrical Diamond Chain
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a
symmetrical diamond chain were analyzed. Due to the separable nature of the
Ising-type exchange interactions between neighboring Heisenberg dimers,
calculation of the entanglement can be performed exactly for each individual
dimer. Pairwise thermal entanglement was studied in terms of the isotropic
Ising-Heisenberg model, and analytical expressions for the concurrence (as a
measure of bipartite entanglement) were obtained. The effects of external
magnetic field and next-nearest neighbor interaction between nodal
Ising sites were considered. The ground-state structure and entanglement
properties of the system were studied in a wide range of the coupling constant
values. Various regimes with different values of the ground-state entanglement
were revealed, depending on the relation between competing interaction
strengths. Finally, some novel effects, such as the two-peak behavior of
concurrence versus temperature and coexistence of phases with different values
of magnetic entanglement were observed
Thermal Entanglement and Critical Behavior of Magnetic Properties on a Triangulated Kagomé Lattice
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
From the Bloch sphere to phase space representations with the Gottesman-Kitaev-Preskill encoding
In this work, we study the Wigner phase-space representation of qubit states
encoded in continuous variables (CV) by using the Gottesman-Kitaev-Preskill
(GKP) mapping. We explore a possible connection between resources for universal
quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer
states, and negativity of the Wigner function in CV architectures, which is a
necessary requirement for quantum advantage. In particular, we show that the
lowest Wigner logarithmic negativity of qubit states encoded in CV with the GKP
mapping corresponds to encoded stabilizer states, while the maximum negativity
is associated with the most non-stabilizer states, H-type and T-type quantum
states.Comment: (v1) Accepted for publication in the Springer's "Mathematics for
Industry" series. (v2) Typo in the abstract fixed; URL of the conference
where the paper has been presented added: International Symposium on
Mathematics, Quantum Theory, and Cryptography (MQC), held in September 2019
in Fukuoka, Japan (https://www.mqc2019.org/mqc2019/program
Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices
Thermal Entanglement and Critical Behavior of Magnetic Properties on a Triangulated Kagomé Lattice
<p>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.</p