Zeeman Z term

\[ \hat H_{\mathrm{Zeeman}\, z} = \sum_{i} \sum_{\sigma\sigma'}V_{i}^Z c_{i\sigma}^\dagger (\sigma^z)_{\sigma\sigma'} c_{i\sigma'} = \sum_{i}V_{i}^Z\left( \hat n_{i\uparrow} - \hat n_{i\downarrow} \right) = i\sum_{i} \frac{V_{i}^Z}{2}\left( - \gamma_{i\uparrow}^+ \gamma_{i\uparrow}^- + \gamma_{i\downarrow}^+ \gamma_{i\downarrow}^- \right) \]

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#include <ZeemanZTerm.hpp>

Static Public Member Functions
template<class T >
static void	Fill (Hamiltonian< T > &ham, double zeeman, int i)
	Filler. More...

Static Public Attributes
static const std::string	name {"zeemanZ"}

static constexpr size_t	locality {1}

Detailed Description

Zeeman Z term

\[ \hat H_{\mathrm{Zeeman}\, z} = \sum_{i} \sum_{\sigma\sigma'}V_{i}^Z c_{i\sigma}^\dagger (\sigma^z)_{\sigma\sigma'} c_{i\sigma'} = \sum_{i}V_{i}^Z\left( \hat n_{i\uparrow} - \hat n_{i\downarrow} \right) = i\sum_{i} \frac{V_{i}^Z}{2}\left( - \gamma_{i\uparrow}^+ \gamma_{i\uparrow}^- + \gamma_{i\downarrow}^+ \gamma_{i\downarrow}^- \right) \]

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Member Function Documentation

◆ Fill()

template<class T >

static void Spinfull::ZeemanZTerm::Fill	(	Hamiltonian< T > &	ham,
		double	zeeman,
		int	i
	)

inlinestatic

Filler.

Template Parameters

T	matrix type, support for: arma::mat, arma::sp_mat

Parameters

ham	hamiltonian container
zeeman	Zeeman potential value \(V_{i}^Z\)
i	site index

Member Data Documentation

◆ locality

constexpr size_t Spinfull::ZeemanZTerm::locality {1}

static

◆ name

const std::string Spinfull::ZeemanZTerm::name {"zeemanZ"}