A thermal entangled quantum refrigerator based on a two-qubit Heisenberg model with Dzyaloshinskii-Moriya interaction in an external magnetic field

Based on an isotropic two spin-1/2 qubits Heisenberg model with the Dzyaloshinskii-Moriya interaction in an ex- ternal magnetic field, we have constructed an entangled quantum refrigerator. Expressions for the basic thermodynamic quantities, i.e., the heat exchanged, the net work input, and the coefficient of performance, are derived. Some intriguing features and their qualitative explanations in zero and non zero magnetic fields are given. The influence of the thermal entanglement on the refrigerator is investigated. The results obtained here have general significance and will be helpful to understand the performance of an entangled quantum refrigerator.

Thermal quantum discord in Heisenberg models with Dzyaloshinski-Moriya interaction

We study the quantum discord of the bipartite Heisenberg model with the Dzyaloshinski-Moriya （DM） interaction in thermal equilibrium state and discuss the effect of the DM interaction on the quantum discord. The quantum entanglement of the system is also discussed and compared with quantum discord. Our results show that the quantum discord may reveal more properties of the system than quantum entanglement and the DM interaction may play an important role in the Heisenberg model.

Implementation of positive-operator-value measurements for single spin qubit via Heisenberg model

This paper shows that a proposal for implementing all possible two-operator positive-operator-value measurements of single spin qubit can be obtained via introducing another spin qubit as ancilla. The realization process is accomplished from the free evolution of the Heisenberg XX model by considering nearest-neighbour spin interaction. A controlled- NOT gate, which is a significant operator for this scheme is also constructed and the generalisation to multiple-operator is considered finally.

Heisenberg Model in a Rotating Magnetic Field

We study the Hcisenberg moder under the influence of a rotating magnetic field. By using a time- dependent unitary transformation, the time evolution operator for the Schrodinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are caleulated, and are expressed in terms of the solid angle subtended by the closed trace of thc total spin vector, as well as in terms of those of the individual spins.

Quantum steering in Heisenberg models with Dzyaloshinskii–Moriya interactions

In this work, we study the quantum steering in two-qubit Heisenberg models with Dzyaloshinskii–Moriya(DM)interaction and an external magnetic field. We find that the steerable weight(SW) and the critical temperature where SW → 0 can be enhanced by the DM interactions. In the special case where the magnetic field is vanishing and the two spins are ferromagnetically coupled, the DM interaction can tune the zero-temperature SW from zero to a finite value. In addition to the SW, some other measurements used to identify the quantum entanglement and quantum correlations are investigated, i.e., the concurrence, the quantum discord, and the robustness of coherence. In the strong magnetic field limit,our results show that the SW is dramatically different from the other measurements.

Multipartite Entanglement in Heisenberg Model

The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ=±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits.

The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach

Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising-Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal Dz and transverse Dx crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second- and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.

Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J_(1)–J_(2)Heisenberg model

Restricted Boltzmann machine(RBM)has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system.On the other hand,as a shallow neural network,it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions.In order to find a way out of the dilemma,here,we propose to adopt the Green's function Monte Carlo(GFMC)method for which the RBM is used as a guiding wave function.To demonstrate the implementation and effectiveness of the proposal,we have applied the proposal to study the frustrated J_(1)-J_(2)Heisenberg model on a square lattice,which is considered as a typical model with sign problem for quantum Monte Carlo simulations.The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results.This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.

An Improved Finite Temperature Lanczos Method and Its Application to the Spin-1/2 Heisenberg Model on the Kagome Lattice

We present an improvement of the finite temperature Lanczos method in order to apply this method to systems at very low temperature. One proposal is to introduce two steps in this method. In the first step, we use the Chebyshev polynomial expansion to calculate exp(-H/T1) random vector>?at moderate temperature T1. In the second step, we apply the ordinary finite temperature Lanczos method using the calculated state as the initial state of the Lanczos method. Another proposal is to employ a sampling method for selecting a random vector. By this sampling, we can improve an efficiency of calculations. Using the improved finite temperature Lanczos method, we calculate the specific heat of the spin-1/2 Heisenberg model on the kagome lattices of 27 and 30 sites.

Bipartite and Tripartite Entanglement in a Three-Qubit Heisenberg Model

The bipartite and tripartite entanglement in a three-qubit Heisenberg XY model with a nonuniform magnetic field is studied. There are two or four peaks in the concurrence of the bipartite entanglement when the amplitudes of the magnetic fields are. differently distributed between the three qubits. It is very interesting to note that there is no tangle of tripartite entanglement between the three qubits when the amplitudes of the magnetic fieMs are varied. However, the variation of the magnetic field direction can induce the tangle. The tangle is periodic about the angle between the magnetic field and the z axis of the spin.

Entanglement in the Quantum Phase Transition of the Half-Integer Spin One-Dimensional Heisenberg Model

We use the Bethe’s ansatz method to study the entanglement of spinons in the quantum phase transition of half integer spin one-dimensional magnetic chains known as quantum wires. We calculate the entanglement in the limit of the number of particles . We obtain an abrupt change in the entanglement next the quantum phase transition point of the anisotropy parameter ?from the gapped phase ?to gapless phase .

Structure of Essential Spectrum and Discrete Spectrum of the Energy Operator of Three-Magnon Systems in the Isotropic Ferromagnetic Non-Heisenberg Model with Spin One and Nearest-Neighbor Interactions

We consider a three-magnon system in the isotropic ferromagnetic Non-Heisenberg model with spin one and with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in a ν-dimensional lattice are investigated. We obtain the lower and upper estimates for the number of three-magnon bound states of the system.

Pairwise thermal entanglement in a three-qubit Heisenberg XX model with a nonuniform magnetic field and Dzyaloshinski-Moriya interaction

Pairwise thermal entanglement in a three-qubit Heisenberg XX model is investigated when a nonuniform mag- netic field and the Dzyaloshinski-Moriya interaction are included. We find that the nonuniform magnetic field and Dzyaloshinski-Moriya interaction are the more efficient control parameters for the increase of entanglement and critical temperature. For both the nearest neighbour sites and the next nearest neighbour sites, the magnetic field can induce entanglement to a certain extent and the Dzyaloshinski-Moriya interaction can enhance the entanglement to a stable value. The steady value of the nearest neighbour site entanglement C12 is larger than the next nearest neighbour site entanglement C13. An interesting phenomenon is that the entanglement curve of C12 appears a peak value when the Dzyaloshinski-Moriya interaction is considered in a nonuniform magnetic field.

Quantum correlation dynamics in a two-qubit Heisenberg XY Z model with decoherence

Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated by making use of concurrence C and quantum discord （QD）. Firstly, we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented： there is an ＂entanglement intermittently sudden death＂ phenomenon in the concurrence but not in the QD, which is valid for all the initial states of this system. Also, the interval time of entanglement sudden death is found to be strongly dependent on the initial states, the inhomogeneous magnetic field b and the anisotropic parameter △. Then, it implies that the steady concurrence and QD can be obtained in the long-time limit, which means that the environmental decoherence cannot entirely destroy the quantum correlation, the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot. In addition, based on the analysis of the steady concurrence and QD with t →∞, we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and .4, whereas the parameter b is independent of the steady concurrence and QD.

Effects of Dzyaloshinski-Moriya interaction and intrinsic decoherence on teleportation via a two-qubit Heisenberg XYZ model

Quantum teleportation via the entangled channel composed of a two-qubit Heisenberg XYZ model with Dzyaloshinski-Moriya （DM） interaction in the presence of intrinsic decoherence has been investigated. We find that the initial state of the channel plays an important role in the teleported state and the average fidelity of teleportation. When the initial channel is in the state ｜ψ1 （0）〉 = a｜00〉 ＋ b｜11〉, the average fidelity is equal to 1/3 constantly, which is independent of the DM interaction and the intrinsic decoherence effect. But when the channel is initially in the state ｜ψ2（0）〉 = a｜01〉 ＋ b｜10〉, the average fidelity is always larger than 2/3. Moreover, under a certain condition, the average fidelity can be enhanced by adjusting the DM interaction, and the intrinsic decoherence leads to a suppression of the fluctuation of the average fidelity.

Entanglement evolution in an anisotropic two-qubit Heisenberg XYZ model with Dzyaloshinskii-Moriya interaction

This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii-Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cosθ｜00〉 ＋ sinθ ｜11〉 and cos Ф ｜01〉 ＋ sin Ф10〉 at zero temperature. The influences of Dzyaloshinskii Moriya interaction D, anisotropic parameter △ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii-Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos Ф ｜01〉 sinФ｜10〉. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii-Moriya interaction D, depends on the anisotropic parameter △ and the environment coupling strength.

Bipartite entanglement in spin-1/2 Heisenberg model

The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if △ 〈γ- 1, and it may keep a steady value of 0.5 in the region of B 〈 J[（△＋ 1）2 -γ^2]^1/2 if △ 〉γ-1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or△=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when △ 〉 △c （△c =γ- 1 and （γ^2 - 1）/2 for the 2- and 3-spin model respectively） and extends in terms of B and T as A increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as △ increases.

Decoherence Effect in An Anisotropic Two-Qubit Heisenberg XYZ Model with Inhomogeneous Magnetic Field

Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ｜01） ＋ sin θ｜10） at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death （ESD） and entanglement sudden birth （ESB） appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B, anisotropic parameter △ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.

Thermal Spin Squeezing as a Signature of Thermal Global Entanglement in Heisenberg Models

We study thermal spin squeezing (TSS) and thermal global entanglement (TGE) in a general Heisenberg spin chain, in the presence of Dzyaloshinskii-Moriya interaction and an external magnetic field. We derive an inequality associating the squeezing parameter and the global concurrence, which establishes (TSS) as a signature of (TGE). The inequality reduces to equality for particular symmetric chains which also associates TSS with bipartite entanglement in such systems. We also check the results by presenting two numerical examples.

Modified Heisenberg Ferromagnet Model and Integrable Equation

We investigate some integrable modified Heisenberg ferromagnet models by using the prolongation structure theory. Through associating them with the motion of curve in Minkowski space, the corresponding coupled integrable equations are presented.