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A first general restructuration of the doc according to the pattern [tour|tutorial|reference]. In the reference part, objects are documented per topic. In each topic, [definition|c++|python|hdf5] (not yet implemented)
56 lines
1.6 KiB
ReStructuredText
56 lines
1.6 KiB
ReStructuredText
.. _hilbert_transform:
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.. module:: pytriqs.dos.hilbert_transform
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Hilbert Transform
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=======================================
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TRIQS comes with a Hilbert transform. Let us look at an example:
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.. runblock:: python
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from pytriqs.lattice.tight_binding import *
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from pytriqs.dos import HilbertTransform
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from pytriqs.gf.local import GfImFreq
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# Define a DOS (here on a square lattice)
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BL = BravaisLattice(units = [(1,0,0) , (0,1,0) ], orbital_positions= [(0,0,0)] )
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t = -1.00 # First neighbour Hopping
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tp = 0.0*t # Second neighbour Hopping
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hop= { (1,0) : [[ t]],
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(-1,0): [[ t]],
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(0,1) : [[ t]],
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(0,-1): [[ t]],
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(1,1) : [[ tp]],
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(-1,-1): [[ tp]],
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(1,-1): [[ tp]],
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(-1,1): [[ tp]]}
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TB = TightBinding (BL, hop)
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d = dos(TB, n_kpts= 500, n_eps = 101, name = 'dos')[0]
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#define a Hilbert transform
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H = HilbertTransform(d)
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#fill a Green function
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G = GfImFreq(indices = ['up','down'], beta = 20)
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Sigma0 = GfImFreq(indices = ['up','down'], beta = 20); Sigma0.zero()
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G <<= H(Sigma = Sigma0,mu=0.)
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Given a density of states `d` (here for a tight-binding model), the Hilbert transform `H` is defined is defined in the following way::
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H = HilbertTransform(d)
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To construct a Green's function::
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G = GfImFreq(indices = ['up','down'], beta = 20)
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Sigma0 = GfImFreq(indices = ['up','down'], beta = 20); Sigma0.zero()
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G <<= H(Sigma = Sigma0, mu=0.)
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.. autoclass:: pytriqs.dos.HilbertTransform
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:members: __call__
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:undoc-members:
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