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This document specifies a proposal for the new low-level system format in Kwant-2.0.
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This document specifies a proposal for the new low-level system format in Kwant-2.
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The requirements are:
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+ Efficient evaluation and construction of the Hamiltonian matrix
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+ Efficient evaluation of submatrices of the Hamiltonian (e.g. all elements which
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The difference between finite and infinite systems is that the latter have a discrete
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*translational symmetry*. In Kwant-2 the translational symmetry is characterised by N linearly
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independent real-space vectors (as opposed to a single realspace vector, as in Kwant-1).
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There is an isomorphism from the symmetry group to `(Z^N, +)`, the additive group of
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There is an isomorphism from the symmetry group `G` to `(Z^N, +)`, the additive group of
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N-tuples of integers.
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We define the infinite sets `S` and `T` respectively to be the sets of all the sites and hoppings in
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the system. We define the finite sets, `S'`, of sites, and `T'`, of hoppings as the quotient sets of
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`S` and `T` with respect to the equivalence relation defined by the symmetry:
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x ~ y ⇔ ∃ g ∈ G | g·x = y`
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where `g·` denotes the group action of a symmetry group element on a site/hopping. We also define the
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function `where` by:
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where: S → G
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x ↦ g | x = g·y , y ∈ S'
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We can now define the *connection set*, `C`, of a system
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## Implementation of Common Operations
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Here we note down the various common operations that the low-level format has to efficiently support
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