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Mesoscopic quantum transport with quantics tensor cross interpolation
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Perustieteiden korkeakoulu |
Bachelor's thesis
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SCI3103
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en
Pages
29
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Abstract
Recent advances in moiré materials have motivated the development of efficient
numerical methods for modeling quantum transport phenomena. These methods
are essential for studying the electronic properties of moiré systems, particularly
in the mesoscopic regime, where conventional approaches involving the compu-
tation of Green’s functions face significant computational challenges due to the
large size of the Hamiltonian matrices. This thesis explores the use of tensor
network techniques to address these challenges: specifically the integration of
Matrix Product States, Matrix Product Operators, and Quantics Tensor Cross
Interpolation. The work consists of two main studies. First, the effectiveness of
Quantics Tensor Cross Interpolation is validated by reproducing results consistent
with recent literature. Second, it is demonstrated that the combination of these
methods enables efficient computation of Green’s functions for one-dimensional
tight-binding models with varying hopping amplitudes, a scenario relevant to
systems exhibiting the moiré effect. Overall, this thesis highlights the potential of
tensor-based numerical techniques to significantly enhance the scalability and
accuracy of quantum transport simulations in complex many-body systems.