Task_type.yaml

# Preamble: 
# Problemm-solver: 
# Conversation summarizer: 
Construct Kinetic Hamiltonian (continuum version, single-particle): $H=H_0+H_{\rm{int}}$
Construct Kinetic Hamiltonian (continuum version, second-quantized): $H=H_0+H_{\rm{int}}$
Construct Kinetic Hamiltonian (lattice version): $H=H_0+H_{\rm{int}}$
Define each term in Kinetic Hamiltonian (continuum version): $H=H_0+H_{\rm{int}}$
Construct Potential Hamiltonian (continuum version): $H=H_0+H_{\rm{int}}$
Define each term in Potential Hamiltonian (continuum version): $H=H_0+H_{\rm{int}}$
Construct interaction Hamiltonian (real space, lattice version): $H=H_0+H_{\rm{int}}$
Construct interaction Hamiltonian (momentum space): $H=H_0+H_{\rm{int}}$
Convert from single-particle to second-quantized form, return in matrix: FT
Convert from single-particle to second-quantized form, return in summation (expand the matrix): FT
Convert noninteracting Hamiltonian in real space to momentum space (continuum version): FT
Convert noninteracting Hamiltonian in real space to momentum space (lattice version): FT
Convert interacting Hamiltonian in real space to momentum space (lattice version): FT
Particle-hole transformation: FT
Simplify the Hamiltonian in the particle-hole basis: FT
Wick's theorem: Wick's theorem
Extract quadratic term: Wick's theorem
Hartree term only: $H_{\rm{HF}}$
Fock term only: $H_{\rm{HF}}$
Expand interaction: $H_{\rm{HF}}$
Swap the index only: $H_{\rm{HF}}$
Swap the index to combine Hartree and Fock terms: $H_{\rm{HF}}$
Reduce momentum in Hartree term (momentum in BZ + reciprocal lattice): OP
Reduce momentum in Hartree term (momentum in BZ): OP
Reduce momentum in Fock term (momentum in BZ + reciprocal lattice): OP
Reduce momentum in Fock term (momentum in BZ): OP
Combine the Hartree and Fock term: OP
# Construct full Hamiltonian after HF: 
# Mathematical simplify:  inner product expansion: 
# Mathematical simplify:  Euler's formula: 
# Mathematical simplify:  prosthaphaeresis: 
# Mathematical simplify:  Expand the product using Associative property: 
# Mathematical simplify:  Combine using Associative property: 
# Mathematical simplify:  reduce index: