5.2. Full Diagonalization method¶
5.2.1. Overview¶
We generate the matrix of \(\hat{\mathcal H }\) by using the real space configuration
\(| \psi_j \rangle\)(\(j=1\cdots d_{\rm H}\), where \(d_{\rm H}\) is the dimension of the Hilbert space):
\({\mathcal H }_{ij}= \langle \psi_i | \hat {\mathcal H } | \psi_j \rangle\).
By diagonalizing this matrix,
we can obtain all the eigenvalues \(E_{i}\) and eigenvectors \(|\Phi_i\rangle\) (\(i=1 \cdots d_{\rm H}\)).
In the diagonalization, we use a LAPACK routine, such as dsyev or zheev.
We also calculate and output
the expectation values \(A_i \equiv \langle \Phi_i | {\hat A} | \Phi_i\rangle\).
These values are used for the finite-temperature calculations.
5.2.2. Finite-temperature calculations¶
From \(A_i \equiv \langle \Phi_i | {\hat A} | \Phi_i\rangle\), we calculate the finite-temperature properties by using the relation
The calculation should be performed by using the own postscripts.
