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documentation:language_reference:objects:tightbinding:start [2016/09/29 11:42] – created Maurits W. Haverkortdocumentation:language_reference:objects:tightbinding:start [2024/09/18 14:35] (current) – Sina Shokri
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 +{{indexmenu_n>999}}
 +====== Tight binding ======
 +
 +###
 +The object tight-binding defines the tight-binding structure of a crystal or a molecule, including the onsite energy of spin-orbitals and the local and non-local hopping among the spin-orbitals. The tight-binding object can be created directly in Lua using the function //[[documentation:language_reference:functions:NewTightBinding|NewTightBinding()]]// or can be generated from the output of DFT calculation (see, for example, //[[documentation:language_reference:functions:TightBindingDefFromDresdenFPLO|TightBindingDefFromDresdenFPLO()]]//).  
 +The tight-binding objects are used to more efficiently generate cluster Hamiltonians (see //[[documentation:language_reference:functions:CreateClusterHamiltonian|CreateClusterHamiltonian()]]//).
 +
 +For more details see the [[documentation:language_reference:objects:tightbinding:properties:start|properties]] of tight-binding objects.
 +
 +<code Quanty Example.Quanty>
 +-- set parameters
 +dAB = 0.2
 +tnn = 1.1
 +-- create the tight binding Hamiltonian
 +HTB = NewTightBinding()
 +HTB.Name = "dichalcogenide tight binding"
 +HTB.Cell = {{sqrt(3),0,0},
 +            {sqrt(3/4),3/2,0},
 +            {0,0,1}}
 +HTB.Atoms = { {"A", {0,0,0},       {{"p", {"0"}}}},
 +                {"B", {sqrt(3),1,0}, {{"p", {"0"}}}}}
 +HTB.Hopping = {{"A.p","A.p",{         0,   0,0},{{-dAB/2}}},
 +                {"B.p","B.p",{         0,   0,0},{{ dAB/2}}},
 +                {"A.p","B.p",{         0,   1,0},{{ tnn  }}},
 +                {"B.p","A.p",{         0,  -1,0},{{ tnn  }}},
 +                {"A.p","B.p",{ sqrt(3/4),-1/2,0},{{ tnn  }}},
 +                {"B.p","A.p",{-sqrt(3/4), 1/2,0},{{ tnn  }}},
 +                {"A.p","B.p",{-sqrt(3/4),-1/2,0},{{ tnn  }}},
 +                {"B.p","A.p",{ sqrt(3/4), 1/2,0},{{ tnn  }}}
 +                }
 +
 +print("Tight-binding object:")
 +print(HTB)
 + 
 +print("create a periodic cluster Hamiltonian with 4 unit-cells along the z-axis:")
 +HCl = CreateClusterHamiltonian(HTB, {"periodic", {{1,0,0},{0,1,0},{0,0,4}}})
 +print(HCl)
 +</code>
 +###
 +
 +<file Quanty_Output>
 +Tight-binding object:
 +
 +Settings of a tight binding model: dichalcogenide tight binding
 +
 +printout of Crystal Structure
 +Units: 2Pi (g.r=2Pi) Angstrom Absolute atom positions
 +Unit cell parameters:
 +a:       1.7320508       0.0000000       0.0000000
 +b:       0.8660254       1.5000000       0.0000000
 +c:       0.0000000       0.0000000       1.0000000
 +Reciprocal latice:
 +a:       3.6275987      -2.0943951       0.0000000
 +b:       0.0000000       4.1887902       0.0000000
 +c:       0.0000000       0.0000000       6.2831853
 +Number of atoms 2
 +#   0 | A ( 0 ) at position {       0.0000000 ,       0.0000000 ,       0.0000000 }
 +      | p shell with 1 orbitals { 0 }
 +#   1 | B ( 5 ) at position {       1.7320508 ,       1.0000000 ,       0.0000000 }
 +      | p shell with 1 orbitals { 0 }
 +Containing a total number of 2 orbitals
 +Hopping definitions ( 8 )
 +Hopping from 0 : A - p to 0 : A - p with translation vector in unit cells: { 0 , 0 , 0 } ({ 0.00000000E+00  0.00000000E+00  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0] -1.00000000E-01 
 +
 +Hopping from 1 : B - p to 1 : B - p with translation vector in unit cells: { 0 , 0 , 0 } ({ 0.00000000E+00  0.00000000E+00  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0]  1.00000000E-01 
 +
 +Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { -1 , 0 , 0 } ({ 0.00000000E+00  1.00000000E+00  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0]  1.10000000E+00 
 +
 +Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 1 , 0 , 0 } ({ 0.00000000E+00 -1.00000000E+00  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0]  1.10000000E+00 
 +
 +Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { 0 , -1 , 0 } ({ 8.66025404E-01 -5.00000000E-01  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0]  1.10000000E+00 
 +
 +Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 0 , 1 , 0 } ({-8.66025404E-01  5.00000000E-01  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0]  1.10000000E+00 
 +
 +Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { -1 , -1 , 0 } ({-8.66025404E-01 -5.00000000E-01  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0]  1.10000000E+00 
 +
 +Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 1 , 1 , 0 } ({ 8.66025404E-01  5.00000000E-01  0.00000000E+00 })
 +Matrix =
 +Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums])
 +          [           0]
 +[     0]  1.10000000E+00 
 +
 +
 +
 +create a periodic cluster Hamiltonian with 4 unit-cells along the z-axis:
 +
 +Operator: Operator
 +QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
 +MaxLength        =          2 (largest number of product of lader operators)
 +NFermionic modes =          8 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)
 +NBosonic modes   =          0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
 +
 +Operator of Length   2
 +QComplex      =          0 (Real==0 or Complex==1)
 +N             =         16 (number of operators of length   2)
 +C  0 A  0 | -1.00000000000000E-01
 +C  1 A  1 |  1.00000000000000E-01
 +C  0 A  1 |  3.30000000000000E+00
 +C  1 A  0 |  3.30000000000000E+00
 +C  2 A  2 | -1.00000000000000E-01
 +C  3 A  3 |  1.00000000000000E-01
 +C  2 A  3 |  3.30000000000000E+00
 +C  3 A  2 |  3.30000000000000E+00
 +C  4 A  4 | -1.00000000000000E-01
 +C  5 A  5 |  1.00000000000000E-01
 +C  4 A  5 |  3.30000000000000E+00
 +C  5 A  4 |  3.30000000000000E+00
 +C  6 A  6 | -1.00000000000000E-01
 +C  7 A  7 |  1.00000000000000E-01
 +C  6 A  7 |  3.30000000000000E+00
 +C  7 A  6 |  3.30000000000000E+00
 +</file>
 +
 +===== Table of contents =====
 +{{indexmenu>.#1|msort}}
  

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