7.1. Overview¶

This document is the manual for the utility to perform the Fourier transformation of the correlation function in the site representation generated by mVMC or $H Φ$ .

7.1.1. Prerequisite¶

The prerequisite of this utility is the same as that of mVMC or $H Φ$ .

7.1.2. Supported quantities¶

This utility supports the Fourier transformation of the following quantities:

One-body correlations

\begin{aligned} ⟨ {\hat{c}}_{k α ↑}^{†} {\hat{c}}_{k β ↑} ⟩ & \equiv \sum_{R}^{N_{R}} e^{- i k \cdot R} ⟨ {\hat{c}}_{0 α ↑}^{†} {\hat{c}}_{R β ↑} ⟩ \\ ⟨ {\hat{c}}_{k α ↓}^{†} {\hat{c}}_{k β ↓} ⟩ & \equiv \sum_{R}^{N_{R}} e^{- i k \cdot R} ⟨ {\hat{c}}_{0 α ↓}^{†} {\hat{c}}_{R β ↓} ⟩ \end{aligned}

Density-density correlation

(7.2)¶

\begin{array}{r} ⟨ {\hat{ρ}}_{k α} {\hat{ρ}}_{k β} ⟩ \equiv \frac{1}{N_{R}} \sum_{R}^{N_{R}} e^{- i k \cdot R} ⟨ ({\hat{ρ}}_{0 α} - ⟨ {\hat{ρ}}_{0 α} ⟩) ({\hat{ρ}}_{R β} - ⟨ {\hat{ρ}}_{R β} ⟩) ⟩ \end{array}

Spin-Spin correlations

\begin{aligned} ⟨ {\hat{S}}_{k α}^{z} {\hat{S}}_{k β}^{z} ⟩ & \equiv \frac{1}{N_{R}} \sum_{R}^{N_{R}} e^{- i k \cdot R} ⟨ {\hat{S}}_{0 α}^{z} {\hat{S}}_{R β}^{z} ⟩ \\ ⟨ {\hat{S}}_{k α}^{+} {\hat{S}}_{k β}^{-} ⟩ & \equiv \frac{1}{N_{R}} \sum_{R}^{N_{R}} e^{- i k \cdot R} ⟨ {\hat{S}}_{0 α}^{+} {\hat{S}}_{R β}^{-} ⟩ \\ ⟨ {\hat{S}}_{k α} \cdot {\hat{S}}_{k β} ⟩ & \equiv \frac{1}{N_{R}} \sum_{R}^{N_{R}} e^{- i k \cdot R} ⟨ {\hat{S}}_{0 α} \cdot {\hat{S}}_{R β} ⟩ \end{aligned}

7.1. Overview¶

7.1.1. Prerequisite¶

7.1.2. Supported quantities¶

Navigation

Related Topics