.. include:: ../../bib/ref.txt .. _HOwToStandard: Input files for Standard mode ============================= An example of input file for the standard mode is shown below: :: W = 2 L = 4 model = "spin" lattice = "triangular lattice" //mu = 1.0 // t = -1.0 // t' = -0.5 // U = 8.0 //V = 4.0 //V'=2.0 J = -1.0 J'=-0.5 // ncond = 8 **Basic rules for input files** - In each line, there is a set of a keyword (before an " ``=``") and a parameter(after an " ``=``"); they are separated by " ``=``". - You can describe keywords in a random order. - Empty lines and lines beginning in a "``//``"(comment outs) are skipped. - Upper- and lowercase are not distinguished. Double quotes and blanks are ignored. - There are three kinds of parameters. 1. Parameters that must be specified (if not, ``vmcdry.out`` will stop with error messages), 2. Parameters that are not necessary be specified (if not, default values are used), 3. Parameters that must not be specified (if specified, ``vmcdry.out`` will stop with error messages). An example of 3 is transfer :math:`t` for the Heisenberg spin system. If you choose "model=spin", you should not specify ":math:`t`". We explain each keyword as follows: Parameters about the kind of a calculation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - ``model`` **Type :** String (Choose from ``"Fermion Hubbard"``, ``"Spin"``, ``"Kondo Lattice"`` , ``"Fermion HubbardGC"``, ``"SpinGC"``, ``"Kondo LatticeGC"`` ) [1]_ **Description :** The target model is specified with this parameter; ``"Fermion Hubbard"`` denotes the canonical ensemble of the Fermion in the Hubbard model .. math:: :label: hubbard \begin{aligned} H = -\mu \sum_{i \sigma} c^\dagger_{i \sigma} c_{i \sigma} - \sum_{i \neq j \sigma} t_{i j} c^\dagger_{i \sigma} c_{j \sigma} + \sum_{i} U n_{i \uparrow} n_{i \downarrow} + \sum_{i \neq j} V_{i j} n_{i} n_{j}, \end{aligned} ``"Spin"`` denotes canonical ensemble in the Spin model( :math:`\{\sigma_1, \sigma_2\}={x, y, z}`) .. math:: :label: spin \begin{aligned} H &= -h \sum_{i} S_{i z} - \Gamma \sum_{i} S_{i x} + D \sum_{i} S_{i z} S_{i z} \nonumber \\ &+ \sum_{i j, \sigma_1}J_{i j \sigma_1} S_{i \sigma_1} S_{j \sigma_1}+ \sum_{i j, \sigma_1 \neq \sigma_2} J_{i j \sigma_1 \sigma_2} S_{i \sigma_1} S_{j \sigma_2} , \end{aligned} ``"Kondo Lattice"`` denotes canonical ensemble in the Kondo lattice model .. math:: :label: kondo \begin{aligned} H = - \mu \sum_{i \sigma} c^\dagger_{i \sigma} c_{i \sigma} - t \sum_{\langle i j \rangle \sigma} c^\dagger_{i \sigma} c_{j \sigma} + \frac{J}{2} \sum_{i} \left\{ S_{i}^{+} c_{i \downarrow}^\dagger c_{i \uparrow} + S_{i}^{-} c_{i \uparrow}^\dagger c_{i \downarrow} + S_{i z} (n_{i \uparrow} - n_{i \downarrow}) \right\}. \end{aligned} ``"Fermion HubbardGC"``, ``"SpinGC"``, and ``"Kondo LatticeGC"`` indicate the :math:`S_z`-unconserved Fermion in the Hubbard model [Eqn. :eq:`hubbard` ], the :math:`S_z`-unconserved Spin model [Eqn. :eq:`spin` ], and the :math:`S_z`-unconserved Kondo lattice model [Eqn. :eq:`kondo` ], respectively. Note: Although these flags have a word "GC"(=grandcanonical), the number of electrons are conserved in these system. - ``lattice`` **Type :** String (Choose from ``"Chain Lattice"``, ``"Square Lattice"``, ``"Triangular Lattice"``, ``"Honeycomb Lattice"``, ``"Kagome"``, ``"Ladder"``) **Description :** The lattice shape is specified with this parameter; above words denote the one dimensional chain lattice (Fig. :num:`latticepng` (a)), the two dimensional square lattice (Fig. :num:`latticepng` (b)), the two dimensional triangular lattice (Fig. :num:`latticepng` (c)), the two dimensional anisotropic honeycomb lattice (Fig. :num:`honeycombpng` ), the Kagome Lattice(Fig. :num:`kagomepng` ), and the ladder lattice (Fig. :num:`ladderpng` ), respectively. .. _latticepng: .. figure:: ../../figs/chap04_1_lattice.png :width: 15.00000cm Schematic illustration of (a) one dimensional chain lattice, (b) two dimensional square lattice, and (c) two dimensional triangular lattice. They have :math:`t`, :math:`V`, and :math:`J` as a nearest neighbor hopping, an offsite Coulomb integral, and a spin-coupling constant, respectively (magenta solid lines); They also have :math:`t'`, :math:`V'`, and :math:`J'` as a next nearest neighbor hopping, offsite Coulomb integral, and spin-coupling constant, respectively (green dashed line). .. _honeycombpng: .. figure:: ../../figs/chap04_1_honeycomb.png :width: 15.00000cm Schematic illustration of the anisotropic honeycomb lattice. The first/second/third nearest neighbor hopping integral, spin coupling, and offsite Coulomb integral depend on the bond direction. .. _kagomepng: .. figure:: ../../figs/kagome.png :width: 10.00000cm Schematic illustration of the Kagome lattice. .. _ladderpng: .. figure:: ../../figs/ladder.png :width: 10.00000cm Schematic illustration of the ladder lattice. Parameters for the lattice ~~~~~~~~~~~~~~~~~~~~~~~~~~ Chain lattice ^^^^^^^^^^^^^ Fig. :num:`latticepng` (a) - ``L`` **Type :** Integer **Description :** The length of the chain is specified with this parameter. Ladder lattice ^^^^^^^^^^^^^^ Fig. :num:`ladderpng` - ``L`` **Type :** Integer **Description :** The length of the ladder is specified with this parameter. - ``W`` **Type :** Integer **Description :** The number of the ladder is specified with this parameter. .. _unitlatticepng: .. figure:: ../../figs/chap04_1_unitlattice.png :width: 15.00000cm The shape of the numerical cell when :math:`{\vec a}_0 = (6, 2), {\vec a}_1 = (2, 4)` in the triangular lattice. The region surrounded by :math:`{\vec a}_0` (Magenta dashed arrow) and :math:`{\vec a}_1` (Green dashed arrow) becomes the cell to be calculated (20 sites). Square lattice , Triangular lattice, Honeycomb lattice, Kagome lattice ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Square lattice [Fig. :num:`latticepng` (b)], Triangular lattice[Fig. :num:`latticepng` (c)], Honeycomb lattice(Fig. :num:`honeycombpng` ), Kagome lattice(Fig. :num:`kagomepng` ) In these lattices, we can specify the shape of the numerical cell by using the following two methods. - ``W``, ``L`` **Type :** Integer **Description :** The alignment of original unit cells (dashed black lines in Figs. :num:`latticepng` - :num:`kagomepng` ) is specified with these parameter. - ``a0W``, ``a0L``, ``a1W``, ``a1L`` **Type :** Integer **Description :** We can specify two vectors (:math:`{\vec a}_0, {\vec a}_1`) that surround the numerical cell (Fig. :num:`unitlatticepng` ). These vectors should be specified in the Fractional coordinate. If we use both of these methods, ``vmcdry.out`` stops. We can check the shape of the numerical cell by using a file ``lattice.gp`` (only for square, trianguler, honeycomb, and kagome lattice) which is written in the Standard mode. This file can be read by ``gnuplot`` as follows: .. code-block:: bash $ gnuplot lattice.gp Sublattice ~~~~~~~~~~ By using the following parameters, we can force the pair-orbital symmetrical to the translation of the sublattice. - ``a0Wsub``, ``a0Lsub``, ``a1Wsub``, ``a1Lsub``, ``Wsub``, ``Lsub`` **Type :** Positive integer. In the default setting, ``a0Wsub=a0W``, ``a0Lsub=a0L``, ``a1Wsub=a1W``, ``a1Lsub=a1L``, ``Wsub=W``, and ``Lsub=L``. Namely, there is no sublattice. **Description :** We can specify these parameter as we specify ``a0W``, ``a0L``, ``a1W``, ``a1L``, ``W``, ``L``. If the sublattice is incommensurate with the original lattice, ``vmcdry.out`` stops. Parameters for the Hamiltonian ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A default value is set as :math:`0` unless a specific value is not defined in a description. Table [table\_interactions] shows the parameters for each models. In the case of a complex type, a file format is " *a real part, an imaginary part* " while in the case of a real type, only " *a real part* ". Local terms ^^^^^^^^^^^ - ``mu`` **Type :** Real **Description :** (Hubbard and Kondo lattice model) The chemical potential :math:`\mu` (including the site potential) is specified with this parameter. - ``U`` **Type :** Real **Description :** (Hubbard and Kondo lattice model) The onsite Coulomb integral :math:`U` is specified with this parameter. - ``Jx``, ``Jy``, ``Jz``, ``Jxy``, ``Jyx``, ``Jxz``, ``Jzx``, ``Jyz``, ``Jzy`` **Type :** Real **Description :** (Kondo lattice model) The spin-coupling constant between the valence and the local electrons is specified with this parameter. If the exchange coupling ``J`` is specified in the input file, instead of ``Jx, Jy, Jz``, the diagonal exchange couplings, ``Jx, Jy, Jz``, are set as ``Jx = Jy = Jz = J``. When both the set of exchange couplings (``Jx``, ``Jy``, ``Jz``) and the exchange coupling ``J`` are specified in the input file, ``vmcdry.out`` will stop. - ``h``, ``Gamma``, ``D`` **Type :** Real **Description :** (Spin model) The longitudinal magnetic field, transverse magnetic field, and the single-site anisotropy parameter are specified with these parameters. The single-site anisotropy parameter is not available for ``model=SpinGCBoost``. The non-local terms described below should be specified in different ways depending on the lattice structure: For ``lattice=Ladder``, the non-local terms are specified in the different way from ``lattice=Chain Lattice``, ``Square Lattice``, ``Triangular Lattice``, ``Honeycomb Lattice``, ``Kagome``. Below, the available parameters for each lattice are shown in Table [table\_interactions]. ====================================== ======== ========= ============= ========= ====== ====== Interactions 1D chain 2D square 2D triangular Honeycomb Kagome Ladder ====================================== ======== ========= ============= ========= ====== ====== ``J``, ``t``, ``V`` (simplified) OK OK OK OK OK NG ``J0``, ``t0``, ``V0`` OK OK OK OK OK OK ``J1``, ``t1``, ``V1`` NG OK OK OK OK OK ``J2``, ``t2``, ``V2`` NG NG OK OK OK OK ``J'``, ``t'``, ``V'`` (simplified) OK OK OK OK OK NG ``J0'``, ``t0'``, ``V0'`` OK OK OK OK OK NG ``J1'``, ``t1'``, ``V1'`` NG OK OK OK OK OK ``J2'``, ``t2'``, ``V2'`` NG NG OK OK OK OK ``J''``, ``t''``, ``V''`` (simplified) OK OK OK OK NG NG ``J0''``, ``t0''``, ``V0''`` OK OK OK OK NG NG ``J1''``, ``t1''``, ``V1''`` NG OK OK OK NG NG ``J2''``, ``t2''``, ``V2''`` NG NG OK OK NG NG ====================================== ======== ========= ============= ========= ====== ====== Table: Interactions for each models defined in an input file. We can define spin couplings as matrix format. Non-local terms for Ladder lattice ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Fig. :num:`ladderpng` - ``t0``, ``t1``, ``t1'``, ``t2``, ``t2'`` **Type :** Complex **Description :** (Hubbard and Kondo lattice model) Hopping integrals in the ladder lattice (See Fig. :num:`ladderpng` ) is specified with this parameter. - ``V0``, ``V1``, ``V1'``, ``V2``, ``V2'`` **Type :** Real **Description :** (Hubbard and Kondo lattice model) Offsite Coulomb integrals on the ladder lattice (Fig. :num:`honeycombpng` are specified with these parameters. - ``J0x``, ``J0y``, ``J0z``, ``J0xy``, ``J0yx``, ``J0xz``, ``J0zx``, ``J0yz``, ``J0zy`` - ``J1x``, ``J1y``, ``J1z``, ``J1xy``, ``J1yx``, ``J1xz``, ``J1zx``, ``J1yz``, ``J1zy`` - ``J1'x``, ``J1'y``, ``J1'z``, ``J1'xy``, ``J1'yx``, ``J1'xz``, ``J1'zx``, ``J1'yz``, ``J1'zy`` - ``J2x``, ``J2y``, ``J2z``, ``J2xy``, ``J2yx``, ``J2xz``, ``J2zx``, ``J2yz``, ``J2zy`` - ``J2'x``, ``J2'y``, ``J2'z``, ``J2'xy``, ``J2'yx``, ``J2'xz``, ``J2'zx``, ``J2'yz``, ``J2'zy`` **Type :** Real **Description :** (Spin model) Spin-coupling constants in the ladder lattice (See Fig. :num:`ladderpng` ) are specified with these parameter. If the simplified parameter ``J0`` is specified in the input file instead of the diagonal couplings, ``J0x, J0y, J0z``, these diagonal couplings are set as ``J0x = J0y = J0z = J0``. If both ``J0`` and the set of the couplings (``J0x, J0y, J0z``) are specified, ``vmcdry.out`` will stop. The above rules are also valid for the simplified parameters, ``J1``, ``J1'``, ``J2``, and ``J2'``. Non-local terms for other than Ladder ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Figs. :num:`latticepng` , :num:`honeycombpng` , :num:`kagomepng` - ``t``, ``t0``, ``t1``, ``t2`` **Type :** Complex **Description :** (Hubbard and Kondo lattice model) The nearest neighbor hoppings for each direction (see :num:`fig_chap04_1_lattice` - :num:`fig_kagome` ) are specified with these parameters. If there is no bond dependence of the hoppings, the simplified parameter ``t`` is available to specify ``t0``, ``t1``, and ``t2`` as ``t0 = t1 = t2 = t``. If both ``t`` and the set of the hoppings (``t0``, ``t1``, ``t2``) are specified, the program will stop. - ``t'``, ``t0'``, ``t1'``, ``t2'`` **Type :** Complex **Description :** (Hubbard and Kondo lattice model) The second nearest neighbor hoppings for each direction (see :num:`fig_chap04_1_lattice` - :num:`fig_kagome` ) are specified with these parameter. If there is no bond dependence of the hoppings, the simplified parameter ``t'`` is available to specify ``t0'``, ``t1'``, and ``t2'`` as ``t0' = t1' = t2' = t'``. If both ``t'`` and the set of the hoppings (``t0'``, ``t1'``, ``t2'``) are specified, the program will stop. - ``t''``, ``t0''``, ``t1''``, ``t2''`` **Type :** Complex **Description :** (Hubbard and Kondo lattice model) The third nearest neighbor hoppings for each direction (see :num:`fig_chap04_1_lattice` - :num:`fig_kagome` ) are specified with these parameter. If there is no bond dependence of the hoppings, the simplified parameter ``t''`` is available to specify ``t0''``, ``t1''``, and ``t2''`` as ``t0'' = t1'' = t2'' = t''``. If both ``t''`` and the set of the hoppings (``t0''``, ``t1''``, ``t2''``) are specified, the program will stop. - ``V``, ``V0``, ``V1``, ``V2`` **Type :** Real **Description :** (Hubbard and Kondo lattice model) The nearest neighbor offsite Coulomb integrals :math:`V` for each direction (see :num:`fig_chap04_1_lattice` - :num:`fig_kagome` ) are specified with these parameters. If there is no bond dependence of the offsite Coulomb integrals, the simplified parameter ``V`` is available to specify ``V0``, ``V1``, and ``V2`` as ``V0 = V1 = V2 = V``. If both ``V`` and the set of the Coulomb integrals (``V0``, ``V1``, ``V2``) are specified, the program will stop. - ``V'``, ``V0'``, ``V1'``, ``V2'`` **Type :** Real **Description :** (Hubbard and Kondo lattice model) The second nearest neighbor-offsite Coulomb integrals :math:`V'` for each direction (see :num:`fig_chap04_1_lattice` - :num:`fig_kagome` ) are specified with this parameter. If there is no bond dependence of the offsite Coulomb integrals, the simplified parameter ``V'`` is available to specify ``V0'``, ``V1'``, and ``V2'`` as ``V0' = V1' = V2' = V'``. If both ``V'`` and the set of the Coulomb integrals (``V0'``, ``V1'``, ``V2'``) are specified, the program will stop. - ``V''``, ``V0''``, ``V1''``, ``V2''`` **Type :** Real **Description :** (Hubbard and Kondo lattice model) The third nearest neighbor-offsite Coulomb integrals :math:`V'` for each direction (see :num:`fig_chap04_1_lattice` - :num:`fig_kagome` ) are specified with this parameter. If there is no bond dependence of the offsite Coulomb integrals, the simplified parameter ``V''`` is available to specify ``V0''``, ``V1''``, and ``V2''`` as ``V0'' = V1'' = V2'' = V''``. If both ``V''`` and the set of the Coulomb integrals (``V0''``, ``V1''``, ``V2''``) are specified, the program will stop. - ``J0x``, ``J0y``, ``J0z``, ``J0xy``, ``J0yx``, ``J0xz``, ``J0zx``, ``J0yz``, ``J0zy`` - ``J1x``, ``J1y``, ``J1z``, ``J1xy``, ``J1yx``, ``J1xz``, ``J1zx``, ``J1yz``, ``J1zy`` - ``J2x``, ``J2y``, ``J2z``, ``J2xy``, ``J2yx``, ``J2xz``, ``J2zx``, ``J2yz``, ``J2zy`` **Type :** Real **Description :** (Spin model) Nearest-neighbor exchange couplings for each direction are specified with thees parameters. If the simplified parameter ``J0`` is specified, instead of ``J0x, J0y, J0z``, the exchange couplings, ``J0x, J0y, J0z``, are set as ``J0x = J0y = J0z = J0``. If both ``J0`` and the set of the exchange couplings (``J0x, J0y, J0z``) are specified, ``vmcdry.out`` will stop. The above rules are valid for ``J1`` and ``J2``. If there is no bond dependence of the nearest-neighbor exchange couplings, the simplified parameters, ``Jx``, ``Jy``, ``Jz``, ``Jxy``, ``Jyx``, ``Jxz``, ``Jzx``, ``Jyz``, ``Jzy``, are available to specify the exchange couplings for every bond as ``J0x = J1x = J2x = Jx``. If any simplified parameter (``Jx`` :math:`\sim` ``Jzy``) is specified in addition to its counter parts (``J0x`` :math:`\sim` ``J2zy``), ``vmcdry.out`` will stop. Below, examples of parameter sets for nearest-neighbor exchange couplings are shown. - If there are no bond-dependent, no anisotropic and offdiagonal exchange couplings (such as :math:`J_{x y}`), please specify ``J`` in the input file. - If there are no bond-dependent and offdiagonal exchange couplings but are anisotropic couplings, please specify the non-zero couplings in the diagonal parameters, ``Jx, Jy, Jz``. - If there are no bond-dependent exchange couplings but are anisotropic and offdiagonal exchange couplings, please specify the non-zero couplings in the nine parameters, ``Jx, Jy, Jz, Jxy, Jyz, Jxz, Jyx, Jzy, Jzx``. - If there are no anisotropic and offdiagonal exchange couplings, but are bond-dependent couplings, please specify the non-zero couplings in the three parameters, ``J0, J1, J2``. - If there are no anisotropic exchange couplings, but are bond-dependent and offdiagonal couplings, please specify the non-zero couplings in the nine parameters, ``J0x, J0y, J0z, J1x, J1y, J1z, J2x, J2y, J2z``. - If there are bond-dependent, anisotropic and offdiagonal exchange couplings, please specify the non-zero couplings in the twenty-seven parameters from ``J0x`` to ``J2zy``. - ``J'x``, ``J'y``, ``J'z``, ``J'xy``, ``J'yx``, ``J'xz``, ``J'zx``, ``J'yz``, ``J'zy`` - ``J0'x``, ``J0'y``, ``J0'z``, ``J0'xy``, ``J0'yx``, ``J0'xz``, ``J0'zx``, ``J0'yz``, ``J0'zy`` - ``J1'x``, ``J1'y``, ``J1'z``, ``J1'xy``, ``J1'yx``, ``J1'xz``, ``J1'zx``, ``J1'yz``, ``J1'zy`` - ``J2'x``, ``J2'y``, ``J2'z``, ``J2'xy``, ``J2'yx``, ``J2'xz``, ``J2'zx``, ``J2'yz``, ``J2'zy`` **Type :** Real **Description :** (Spin model) The second nearest neighbor exchange couplings are specified. However, for ``lattice = Honeycomb Lattice`` and ``lattice = Kagome`` with ``model=SpinGCCMA``, the second nearest neighbor exchange couplings are not available in the :math:`Standard` mode. If the simplified parameter ``J'`` is specified, instead of ``J'x, J'y, J'z``, the exchange couplings are set as ``J'x = J'y = J'z = J'``. If both ``J'`` and the set of the couplings (``J'x, J'y, J'z``) are specified, the program will stop. - ``J''x``, ``J''y``, ``J''z``, ``J''xy``, ``J''yx``, ``J''xz``, ``J''zx``, ``J''yz``, ``J''zy`` - ``J0''x``, ``J0''y``, ``J0''z``, ``J0''xy``, ``J0''yx``, ``J0''xz``, ``J0''zx``, ``J0''yz``, ``J0''zy`` - ``J1''x``, ``J1''y``, ``J1''z``, ``J1''xy``, ``J1''yx``, ``J1''xz``, ``J1''zx``, ``J1''yz``, ``J1''zy`` - ``J2''x``, ``J2''y``, ``J2''z``, ``J2''xy``, ``J2''yx``, ``J2''xz``, ``J2''zx``, ``J2''yz``, ``J2''zy`` **Type :** Real **Description :** (Spin model) The third nearest neighbor exchange couplings are specified. However, for ``lattice = Honeycomb Lattice`` and ``lattice = Kagome`` with ``model=SpinGCCMA``, the third nearest neighbor exchange couplings are not available in the :math:`Standard` mode. If the simplified parameter ``J''`` is specified, instead of ``J''x, J''y, J''z``, the exchange couplings are set as ``J''x = J''y = J''z = J''``. If both ``J''`` and the set of the couplings (``J''x, J''y, J''z``) are specified, the program will stop. - ``phase0``, ``phase1`` **Type :** Double (``0.0`` as defaults) **Description :** We can specify the phase for the hopping through the cell boundary with these parameter (unit: degree). These factors for the :math:`\vec{a}_0` direction and the :math:`\vec{a}_1` direction can be specified independently. For the one-dimensional system, only ``phase0`` can be used. For example, a fopping from :math:`i`-th site to :math:`j`-th site through the cell boundary with the positive direction becomes as .. math:: \begin{aligned} \exp(i \times {\rm phase0}\times\pi/180) \times t {\hat c}_{j \sigma}^\dagger {\hat c}_{i \sigma} + \exp(-i \times {\rm phase0}\times\pi/180) \times t^* {\hat c}_{i \sigma}^\dagger {\hat c}_{j \sigma} \end{aligned} Parameters for the numerical condition ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - ``ncond`` **Type :** int-type (must be specified) **Description :** The number of itinerant electrons. It is the sum of the :math:`\uparrow` and :math:`\downarrow` electrons. - ``NVMCCalMode`` **Type :** int-type (default value: 0) **Description :** [0] Optimization of variational parameters, [1] Calculation of one body and two body Green’s functions. - ``NDataIdxStart`` **Type :** int-type (default value: 1) **Description :** An integer for numbering of output files. For ``NVMCCalMode`` = 0 , ``NDataIdxStart`` is added at the end of the output files. For ``NVMCCalMode`` = 1, the files are outputted with the number from ``NDataIdxStart`` to ``NDataIdxStart`` + ``NDataQtySmp``-1. - ``NDataQtySmp`` **Type :** int-type (default value: 1) **Description :** The set number for outputted files (only used for ``NVMCCalMode`` = 1). - ``NSPGaussLeg`` **Type :** int-type (Positive integer, default value is 8 for ``2Sz=0``) **Description :** The mesh number for the Gauss-legendre quadrature about :math:`\beta` integration (:math:`S_y` rotation) for the spin quantum-number projection in actual numerical calculation. - ``NSPStot`` **Type :** int-type ( greater equal 0, default value is 0 for ``2Sz=0``) **Description :** The total spin quantum-number. - ``2Sz`` **Type :** int-type ( greater equal 0, default value is 0) **Description :** The spin quantum-number :math:`S_z`. - ``NMPTrans`` **Type :** int-type (Positive integer. Default ``1``) **Description :** The number of the momentum and lattice translational quantum-number projection. In the case of not to apply the projection, this value must be set as 1. - ``NSROptItrStep`` **Type :** int-type (Positive integer, default value: 1000) **Description :** The whole step number to optimize variational parameters by SR method. Only used for ``NVMCCalMode`` =0. - ``NSROptItrSmp`` **Type :** int-type (Positive integer, default value: ``NSROptItrStep``/10) **Description :** In the ``NSROptItrStep`` step, the average values of the each variational parameters at the ``NSROptItrStep`` step are adopted as the optimized values. Only used for ``NVMCCalMode`` =0. - ``DSROptRedCut`` **Type :** double-type (default value: 0.001) **Description :** The stabilized factor for the SR method by truncation of redundant directions corresponding to :math:`\varepsilon_{\rm wf}` in the ref. [Tahara2008_ ]. - ``DSROptStaDel`` **Type :** double-type (default value: 0.02) **Description :** The stabilized factor for the SR method by modifying diagonal elements in the overwrap matrix corresponding to :math:`\varepsilon` in the ref. [Tahara2008_ ]. - ``DSROptStepDt`` **Type :** double-type (default value: 0.02) **Description :** The time step using in the SR method. - ``NVMCWarmUp`` **Type :** int-type (Positive integer, default value: 10) **Description :** Idling number for the Malkov chain Montecarlo Methods. - ``NVMCInterval`` **Type :** int-type (Positive integer, default value: 1) **Description :** The interval step between samples. The local update will be performed ``Nsite`` × ``NVMCInterval`` times. - ``NVMCSample`` **Type :** int-type (Positive integer, default value: 1000) **Description :** The sample numbers to calculate the expected values. - ``NExUpdatePath`` **Type :** int-type (Positive integer) **Description :** The option for local update about exchange terms. 0: not update, 1: update. The default value is set as 1 when the local spin exists, otherwise 0. - ``RndSeed`` **Type :** int-type (default value: 123456789) **Description :** The initial seed of generating random number. For MPI parallelization, the initial seeds are given by ``RndSeed`` +my rank+1 at each ranks. - ``NSplitSize`` **Type :** int-type (Positive integer, default value: 1) **Description :** The number of processes of MPI parallelization. - ``NStore`` **Type :** int-type (0 or 1, default value: 1) **Description :** The option of applying matrix-matrix product to calculate expected values :math:`\langle O_k O_l \rangle` (0: off, 1: on). This speeds up calculation but increases the amount of memory usage from :math:`O(N_\text{p}^2)` to :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})`, where :math:`N_\text{p}` is the number of the variational parameters and :math:`N_\text{MCS}` is the number of Monte Carlo sampling. - ``NSRCG`` **Type :** int-type (0 or 1, default value: 0) **Description :** The option of solving :math:`Sx=g` in the SR method without constructing :math:`S` matrix [NeuscammanUmrigarChan_ ]. (0: off, 1: on). This reduces the amount of memory usage from :math:`O(N_\text{p}^2) + O(N_\text{p}N_\text{MCS})` to :math:`O(N_\text{p}) + O(N_\text{p}N_\text{MCS})` when :math:`N_\text{p} > N_\text{MCS}`. - ``ComplexType`` **Type :** int-type (``0`` or ``1``. Default value is ``0`` for the :math:`S_z`-conserved system and ``1`` for the :math:`S_z`-unconserved system.) **Description :** If it is ``0``, only the real part of the variational parameters are optimized. And the real and the imaginary part of them are optimized if this parameter is ``1``. - ``OutputMode`` **Type :** Choose from ``"none"``, ``"correlation"``, and ``"full"`` (``correlation`` as a default) **Description :** Indices of correlation functions are specified with this keyword. ``"none"`` indicates correlation functions will not calculated. When ``outputmode="correlation"``, the correlation function supported by the utility ``fourier`` is computed. For more details, see the document in ``doc/fourier/``. If ``"full"`` is selected, :math:`\langle c_{i \sigma}^{\dagger}c_{j \sigma'} \rangle` is computed at all :math:`i, j, \sigma, \sigma'`, and :math:`\langle c_{i_1 \sigma}^{\dagger}c_{i_2 \sigma} c_{i_3 \sigma'}^{\dagger}c_{i_4 \sigma'} \rangle` is computed at all :math:`i_1, i_2, i_3, i_4, \sigma, \sigma'`. In spin system, indices are specified as those on the Bogoliubov representation (See [sec\_bogoliubov\_rep]). - ``CDataFileHead`` **Type :** string-type (default : ``"zvo"``) **Description :** A header for output files. For example, the output filename for one body Green’s function becomes " **xxx\_cisajs\_yyy.dat**" (xxx are characters set by ``CDataFileHead`` and yyy are numbers given by numbers from ``NDataIdxStart`` to ``NDataIdxStart`` + ``NDataQtySmp``). - ``CParaFileHead`` **Type :** string-type (default : ``"zqp"``) **Description :** A header for output files of the optimized variational parameters. For example, the optimized variational parameters are outputted as **zzz\_opt\_yyy.dat** (zzz are characters set by ``CParaFileHead`` and yyy are numbers given by numbers from ``NDataIdxStart`` to ``NDataIdxStart`` + ``NDataQtySmp`` -1). .. [1] GC=Grand Canonical