Perturbative calculations of quantum spin tunneling in effective spin systems with a transversal magnetic field and transversal anisotropy

Krizanac, M; Vedmedenko, E. Y.; Wiesendanger, R.

doi:10.1088/1367-2630/aa5736

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…The ground state energy splitting induced by the quantum tunneling of the spin can be obtained by applying perturbation theory to the SMM Hamiltonian, which is given by

Δ E = \frac{4 s}{2^{2 s} true(2 s - 1 true)! K_{z}^{2 s - 1}} \prod_{n = 1}^{2 s} true(B_{x} - true(2 s + 1 - 2 n true) B_{normala} true)

where B x and K represents the two perturbations, s represents the ground spin state of the SMM and

B_{normala} = \sqrt{2 K K_{z}}

. From Equation we see that the tunnel splitting is zero when

B_{x}^{true(n true)} = true(2 s + 1 - 2 n true) B_{normala}

for n = 1,2,…,2 s .…”

Section: Model Hamiltonianmentioning

confidence: 99%

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

González

2019

Physica Status Solidi (b)

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The electron transport through a single molecule magnet transistor in the presence of a local transverse magnetic field and ac‐driven gate voltage has been considered. The conductance has been calculated as a function of the electron energy and transverse magnetic field by using the Floquet and Landauer formalism. It is shown that the time periodic potential causes zero transmission resonances that oscillate as a function of the transverse magnetic field due to the Berry phase interference associated with two quantum tunneling paths. It has been found that these Berry phase oscillations can be detected in the conductance as a function of the transverse magnetic field for an incoming electron with a specific energy.

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“…The ground state energy splitting induced by the quantum tunneling of the spin can be obtained by applying perturbation theory to the SMM Hamiltonian, which is given by

Δ E = \frac{4 s}{2^{2 s} true(2 s - 1 true)! K_{z}^{2 s - 1}} \prod_{n = 1}^{2 s} true(B_{x} - true(2 s + 1 - 2 n true) B_{normala} true)

where B x and K represents the two perturbations, s represents the ground spin state of the SMM and

B_{normala} = \sqrt{2 K K_{z}}

. From Equation we see that the tunnel splitting is zero when

B_{x}^{true(n true)} = true(2 s + 1 - 2 n true) B_{normala}

for n = 1,2,…,2 s .…”

Section: Model Hamiltonianmentioning

confidence: 99%

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

González

2019

Physica Status Solidi (b)

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“…The degeneracies in the Hamiltonian (8) can be removed by the perturbation δℋ, which do not commute with S 1,z . The energy splitting induced by the quantum tunneling of the spin can be obtained by applying perturbation theory to the Hamiltonian ℋ 0 , which is given by [19][20][21]…”

Section: Density Matrix: Analytical Formulationmentioning

confidence: 99%

“…The degeneracies in the Hamiltonian (8) can be removed by the perturbation

δ ℋ

, which do not commute with

S_{1, z}

. The energy splitting induced by the quantum tunneling of the spin can be obtained by applying perturbation theory to the Hamiltonian

ℋ_{0}

, which is given by [ 19–21 ]

Δ E = \frac{4 s}{2^{2 s} (2 s - 1)! K_{z}^{2 s - 1}} \prod_{n = 1}^{2 s} false(B_{x} - (2 s + 1 - 2 n) B_{normala} false)

where

B_{x}

and K represent the two perturbations, s represents the ground spin state of the SMM, and

B_{normala} = \sqrt{2 K K_{z}}

.…”

Section: Density Matrix: Analytical Formulationmentioning

confidence: 99%

Berry‐Phase Effect in Single‐Molecule Magnets: Analytical and Numerical Results

Anaya-García

Salgado-Blanco

González

2022

Physica Status Solidi (b)

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Herein, transport signatures of quantum interference on the current through a single‐molecule magnet transistor tunnel coupled to oppositely polarized leads in the presence of a local transverse and longitudinal magnetic field are theoretically and numerically investigated. These calculations are based on a density matrix approach where the ground‐state energy splitting induced by tunneling of the spin between different paths is treated with the aid of perturbation theory. Using this approach, it is shown that it is possible to use an effective Hamiltonian, which describes the Berry‐phase interference as a function of the transverse magnetic field, which completely blocks the current flow when the single‐molecule magnet is placed between oppositely polarized leads. Finally, this effective Hamiltonian is used in an open‐source Python software (QmeQ) that allows us to calculate the current through the single‐molecule magnet with oppositely polarized leads tunnel coupled to the single‐molecule magnet. The analytical results are well reproduced by numerical simulations.

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“…Quantum spin tunneling is phenomena where single spin tunnels between two opposite directions. This leads to degeneracy of energy levels related with opposite states which is called quantum spin tunneling splitting (see, for instance, [15,16]). Experimental observation of quantum tunneling of the magnetization of cluster with S = 10 was reported in [17].…”

Section: Introductionmentioning

confidence: 99%

Observation of spin-1 tunneling on a quantum computer

Gnatenko¹,

Tkachuk²

2022

Preprint

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Spin-1 tunneling and splitting of energy levels as a result of tunneling are observed explicitly on IBM's quantum computer, ibmq-bogota. The spin-1 is realized with two spins-1/2. We detect oscillations of spin-1 between the states |1 , | − 1 in the result of tunneling on the basis of studies of the time dependence of the mean value of zcomponent of spin-1 on the quantum device. The energy level splitting is observed quantifying on the IBM's quantum computer the eigenvalues of Hamiltonian which describes the spin tunneling.

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Perturbative calculations of quantum spin tunneling in effective spin systems with a transversal magnetic field and transversal anisotropy

Cited by 6 publications

References 19 publications

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

Berry‐Phase in a Periodically Driven Single Molecule Magnet Transistor

Berry‐Phase Effect in Single‐Molecule Magnets: Analytical and Numerical Results

Observation of spin-1 tunneling on a quantum computer

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