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International Journal of New Findings in Engineering Science and Technology

Monte Carlo simulation of distance dependent quantum entanglement in mixed XXZ Heisenberg spin-1/2 chains

İzzet Paruğ Duru

Published Sep 27, 2024• 0 citations
Publisher

Abstract

The quantum entanglement of mixed XXZ Heisenberg spin-1/2 chain is examined. We quantify localizable entanglement (LE) in terms of upper/lower bounds through Quantum Monte Carlo simulations. Loop algorithm is chosen to numerically calculate thermodynamic quantities including spin-spin correlations. The exchange coupling, Zeeman energy, and dipolar interaction are literally taken into account. Findings summarize that the strength of dipole-dipole interaction (D) and external magnetic field (Bz) are notable in entanglement formation driving creation and extinction of entanglement. The creation and extinction of entanglement depend on D and Bz. Furthermore, strong fields at the critical temperatures lead a non-monotonic/monotonic behavior introducing revival phenomena. Nevertheless, strong D provides the distance-dependent stability of LE values, preserving unity.

DOI
10.61150/ijonfest.2024020206

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The quantum entanglement of mixed XXZ Heisenberg spin-1/2 chain is examined. We quantify localizable entanglement (LE) in terms of upper/lower bounds through Quantum Monte Carlo simulations. Loop algorithm is chosen to numerically calculate thermodynamic quantities including spin-spin correlations. The exchange coupling, Zeeman energy, and dipolar interaction are literally taken into account. Findings summarize that the strength of dipole-dipole interaction (D) and external magnetic field (Bz) are notable in entanglement formation driving creation and extinction of entanglement. The creation and extinction of entanglement depend on D and Bz. Furthermore, strong fields at the critical temperatures lead a non-monotonic/monotonic behavior introducing revival phenomena. Nevertheless, strong D provides the distance-dependent stability of LE values, preserving unity.
The entanglement of the ferromagnetically ordered isotropic spin-1/2 chain is discussed. The analytically deriving concurrence of a two-qubit state allows focusing on the effect of dipolar interaction (D). Low fields enable tuning creation/extinction of entangled states, particularly at low temperatures. There is a joint effect of the applied field and dipolar interaction which can’t be disregarded. We perform Quantum Monte Carlo simulations on quantifying localizable entanglement (LE) in terms of upper/lower bounds. Findings reveal that D and B_z are decisive parameters on the production of entanglement including creation and extinction. A non-monotonic behavior has occurred under high fields at the critical temperature. However, strong D provides the stability of LE values concerning distance herewith conserving the unity at low temperatures under zero field. Rival regions are observed for the distant nearest neighbors, particularly odd ones.
The bounds of entanglement on antiferromagnetic (AF) isotropic Heisenberg spin-1/2 chain including dipole- dipole interaction (D) were investigated. The Quantum Monte Carlo method based on loop algorithm was employed to calculate the two-spin and single-spin expectation values mediating the lower and upper bounds. It was revealed that D and Bz (the applied magnetic field) were pivotal parameters in controlling either entanglement creation/extinction or entanglement enhancement/weakening. Rival regions indicated a revival phenomenon depending on the temperature for various strengths of D which also showed a nonmonotonic behavior under certain Bz identifying critical points. Even if thermal agitations break the stability of strong D entanglement, it remains invariable at very low temperatures.
We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of localizable entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1∕21∕21∕2 and spin-1 systems, we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.
Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.