Ad
A.J. de Bruyn
info
Please Note
<p>This page displays the records of the person named above and is not linked to a unique person identifier. This record may need to be merged to a profile.</p>
1 records found
1
In this thesis we implement the Lindblad equation in the matrix product state (MPS) formalism using an operator splitting method. We developed a second-order method based on a Trotter approximation and a third-order high-dimensional midpoint method and we proposed a new fourth-order method based on Duhamel’s principle and a nested RK4 method, all of which preserve positivity and Hermiticity of the density operator. We simulated spin transport through an XXZ-Hamiltonian Heisenberg chain, for which we found the magnetisation profile and measured a spin current of 0.04-0.05. The results obtained are consistent with the existing literature. The extensive error analysis shows that the time step ∆t is the main contributor to the error, if the bond dimension χ is set to at least 15. The third-order method is in general preferred to the second-order method, as only this method preserves trace. We also analysed the Hubbard model, including a spin orbit coupling, in order to propose a method for simulating the chiral induced spin selectivity (CISS) effect.
...
In this thesis we implement the Lindblad equation in the matrix product state (MPS) formalism using an operator splitting method. We developed a second-order method based on a Trotter approximation and a third-order high-dimensional midpoint method and we proposed a new fourth-order method based on Duhamel’s principle and a nested RK4 method, all of which preserve positivity and Hermiticity of the density operator. We simulated spin transport through an XXZ-Hamiltonian Heisenberg chain, for which we found the magnetisation profile and measured a spin current of 0.04-0.05. The results obtained are consistent with the existing literature. The extensive error analysis shows that the time step ∆t is the main contributor to the error, if the bond dimension χ is set to at least 15. The third-order method is in general preferred to the second-order method, as only this method preserves trace. We also analysed the Hubbard model, including a spin orbit coupling, in order to propose a method for simulating the chiral induced spin selectivity (CISS) effect.