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documentation:language_reference:objects:tightbinding:start [2024/09/13 21:42] – Maurits W. Haverkort | documentation:language_reference:objects:tightbinding:start [2024/09/18 14:35] (current) – Sina Shokri | ||
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### | ### | ||
- | Operators define quantum mechanical operators implemented in second quantization. The most general operator one can implement is: | + | 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 |
- | $$ \begin{align} | + | The tight-binding objects are used to more efficiently generate cluster Hamiltonians |
- | O& | + | |
- | & | + | |
- | & | + | |
- | & + \sum_{\tau_1, | + | |
- | &+ \dots | + | |
- | \end{align} $$ | + | |
- | Note that as $a^{\dagger}_{\tau_1}a^{\phantom{\dagger}}_{\tau_2} = \delta_{\tau_1, | + | |
- | ### | + | |
- | ### | + | For more details see the [[documentation: |
- | Operators can act on Fermions and Bosons. An operator //O// has //O.NF// Fermions and //O.NB// Bosons. The Fermions are indexed from //0// to // | + | |
- | ### | + | |
+ | <code Quanty Example.Quanty> | ||
+ | -- set parameters | ||
+ | dAB = 0.2 | ||
+ | tnn = 1.1 | ||
+ | -- create the tight binding Hamiltonian | ||
+ | HTB = NewTightBinding() | ||
+ | HTB.Name = " | ||
+ | HTB.Cell = {{sqrt(3), | ||
+ | {sqrt(3/ | ||
+ | {0,0,1}} | ||
+ | HTB.Atoms = { {" | ||
+ | {" | ||
+ | HTB.Hopping = {{" | ||
+ | {" | ||
+ | {" | ||
+ | {" | ||
+ | {" | ||
+ | {" | ||
+ | {" | ||
+ | {" | ||
+ | } | ||
- | ===== Table of contents ===== | + | print(" |
- | {{indexmenu> | + | print(HTB) |
+ | |||
+ | print(" | ||
+ | HCl = CreateClusterHamiltonian(HTB, | ||
+ | print(HCl) | ||
+ | </ | ||
+ | ### | ||
- | ==== Result ==== | ||
<file Quanty_Output> | <file Quanty_Output> | ||
- | text produced as 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: | ||
+ | b: | ||
+ | c: | ||
+ | Reciprocal latice: | ||
+ | a: | ||
+ | b: | ||
+ | c: | ||
+ | Number of atoms 2 | ||
+ | # 0 | A ( 0 ) at position { | ||
+ | | p shell with 1 orbitals { 0 } | ||
+ | # 1 | B ( 5 ) at position { | ||
+ | | 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 | ||
+ | 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 | ||
+ | Matrix = | ||
+ | Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums]) | ||
+ | [ 0] | ||
+ | [ | ||
+ | |||
+ | Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { -1 , 0 , 0 } ({ 0.00000000E+00 | ||
+ | Matrix = | ||
+ | Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums]) | ||
+ | [ 0] | ||
+ | [ | ||
+ | |||
+ | Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 1 , 0 , 0 } ({ 0.00000000E+00 -1.00000000E+00 | ||
+ | Matrix = | ||
+ | Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums]) | ||
+ | [ 0] | ||
+ | [ | ||
+ | |||
+ | Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { 0 , -1 , 0 } ({ 8.66025404E-01 -5.00000000E-01 | ||
+ | Matrix = | ||
+ | Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums]) | ||
+ | [ 0] | ||
+ | [ | ||
+ | |||
+ | Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 0 , 1 , 0 } ({-8.66025404E-01 | ||
+ | Matrix = | ||
+ | Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums]) | ||
+ | [ 0] | ||
+ | [ | ||
+ | |||
+ | Hopping from 0 : A - p to 1 : B - p with translation vector in unit cells: { -1 , -1 , 0 } ({-8.66025404E-01 -5.00000000E-01 | ||
+ | Matrix = | ||
+ | Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums]) | ||
+ | [ 0] | ||
+ | [ | ||
+ | |||
+ | Hopping from 1 : B - p to 0 : A - p with translation vector in unit cells: { 1 , 1 , 0 } ({ 8.66025404E-01 | ||
+ | Matrix = | ||
+ | Real Part of Matrix with dimensions [Ni=1][Nj=1] ([Rows][Collums]) | ||
+ | [ 0] | ||
+ | [ | ||
+ | |||
+ | |||
+ | |||
+ | create a periodic cluster Hamiltonian with 4 unit-cells along the z-axis: | ||
+ | |||
+ | Operator: Operator | ||
+ | QComplex | ||
+ | MaxLength | ||
+ | NFermionic modes = 8 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) | ||
+ | NBosonic modes | ||
+ | |||
+ | Operator of Length | ||
+ | QComplex | ||
+ | N | ||
+ | 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 | ||
</ | </ | ||