.. highlight:: none Interaction definition files ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The interaction definition files describe the coefficients :math:`T_{\alpha\beta}(r_{ij})`, :math:`J_{\alpha\beta}(r_{ij})`, :math:`V_{\alpha\beta}(r_{ij})`, or :math:`U_{\alpha}` of the one-body and two-body Hamiltonian denoted by the following expressions. They are given in Wannier90(-like) format. It is noted that the generalized two-body interaction term (InterAll) is not supported in the wave-number space UHF. **Transfer**: :math:`\sum_{ij\alpha\beta\sigma} T_{\alpha\beta}(r_{ij})\,c_{i\alpha\sigma}^{\dagger}c_{j\beta\sigma}^{\phantom{\dagger}}` **CoulombIntra**: :math:`\sum_{i\alpha} U_\alpha\,n_ {i\alpha\uparrow} n_{i\alpha\downarrow}, \quad (n_{i\alpha\sigma}=c_{i\alpha\sigma}^{\dagger}c_{i\alpha\sigma}^{\phantom{\dagger}})` **CoulombInter**: :math:`\sum_{ij\alpha\beta} V_{\alpha\beta}(r_{ij})\,n_{i\alpha} n_{j\beta}, \quad (n_{i\alpha}=n_{i\alpha\uparrow}+n_{i\alpha\downarrow})` **Hund**: :math:`\sum_{ij\alpha\beta} J_{\alpha\beta}^{\rm Hund}(r_{ij}) \left( n_{i\alpha\uparrow} n_{j\beta\uparrow} + n_{i\alpha\downarrow} n_{j\beta\downarrow} \right)` **Ising**: :math:`\sum_{ij\alpha\beta} J_{\alpha\beta}^{\rm Ising}(r_{ij}) S^{z}_{i\alpha} S^{z}_{j\beta}, \quad (S^{z}_{i\alpha}=\frac{1}{2}(n_{i\alpha\uparrow} - n_{i\alpha\downarrow}))` **PairHop**: :math:`\sum_{ij\alpha\beta} J_{\alpha\beta}^{\rm PH}(r_{ij})\,c_{i\alpha\uparrow}^{\dagger} c_{j\beta\uparrow}^{\phantom{\dagger}} c_{i\alpha\downarrow}^{\dagger} c_{j\beta\downarrow}^{\phantom{\dagger}} + \textit{h.c.}` **Exchange**: :math:`\sum_{ij\alpha\beta} J_{\alpha\beta}^{\rm Ex}(r_{ij})\,c_{i\alpha\uparrow}^\dagger c_{j\beta\uparrow}^{\phantom{\dagger}} c_{j\beta\downarrow}^\dagger c_{i\alpha\downarrow}^{\phantom{\dagger}}` **PairLift**: :math:`\sum_{ij\alpha\beta} J_{\alpha\beta}^{\rm PairLift}(r_{ij})\,c_{i\alpha\uparrow}^{\dagger} c_{i\alpha\downarrow}^{\phantom{\dagger}} c_{j\beta\uparrow}^{\dagger} c_{j\beta\downarrow}^{\phantom{\dagger}}` An example of the file is shown below. :: wannier90 format for vmcdry.out or HPhi -sdry 10 245 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ... 1 1 1 1 1 -3 -3 -2 1 1 -0.0000269645 -0.0000000000 -3 -3 -2 1 2 -0.0000071722 -0.0000018600 -3 -3 -2 1 3 -0.0000083990 0.0000010972 -3 -3 -2 1 4 -0.0000000990 0.0000000427 -3 -3 -2 1 5 -0.0000018628 -0.0000003609 -3 -3 -2 1 6 -0.0000129504 -0.0000014047 -3 -3 -2 1 7 -0.0000189169 0.0000024697 -3 -3 -2 1 8 0.0000238115 0.0000014316 -3 -3 -2 1 9 0.0000036708 -0.0000003266 -3 -3 -2 1 10 0.0000361752 0.0000003247 -3 -3 -2 2 1 -0.0000071722 0.0000018600 -3 -3 -2 2 2 0.0000105028 -0.0000000000 ... File format ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - Line 1: Header - Line 2: ``[Norbit]`` - Line 3: ``[Npts]`` - Lines 4 - :math:`\lceil N_\text{pts} / 15 \rceil + 3`: ``[n1] [n2] ...`` - Line :math:`\lceil N_\text{pts} / 15 \rceil + 4` onwards: ``[rx] [ry] [rz] [alpha] [beta] [J.real] [J.imag]`` Parameters ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - ``[Norbit]`` **Type :** Integer **Description :** This parameter specifies the number of orbitals :math:`N_\text{orbit}` in a unit cell. - ``[Npts]`` **Type :** Integer **Description :** This parameter specifies the number of cells in a rectangular cuboid that accommodates entire translation vectors. - ``[n1]``, ``[n2]``, ... **Type :** Integer **Description :** These parameters specify the multiplicity of cells (ordinary 1), with 15 points in a line. - ``[rx]``, ``[ry]``, ``[rz]`` **Type :** Integer **Description :** These parameters specify the translation vector. - ``[alpha]``, ``[beta]`` **Type :** Integer **Description :** These parameters specify the indices of the orbitals. ``[alpha]`` corresponds to the orbital :math:`\alpha` in the original cell, and ``[beta]`` corresponds to the orbital :math:`\beta` in the cell displaced by :math:`\vec{r}`. - ``[J.real]``, ``[J.imag]`` **Type :** Float **Description :** These parameters specify the real and imaginary parts of the coefficient :math:`J_{\alpha\beta}(\vec{r})`. Usage rules ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - Header cannot be omitted. - The unspecified elements of the coefficient matrix are assumed to be zero. - The translation vectors need to be enclosed within the CellShape. If the range of ``r_x``, ``r_y``, or ``r_z`` exceeds the extent of ``x``, ``y``, or ``z`` dimension of CellShape, the program terminates with an error. - When ``mode.enable_spin_orbital`` is set to ``true``, the orbital indices of Transfer term are interpreted as the extended orbital indices including spin degree of freedom that ranges from 1 to :math:`2 N_\text{orbital}`, in which the indices :math:`1 \dots N_\text{orbital}` correspond to spin-up, and the indices :math:`N_\text{orbital}+1 \dots 2N_\text{orbital}` correspond to spin-down. Otherwise, only the entries with the orbital indices from 1 to :math:`N_\text{orbital}` are taken into account. .. raw:: latex