2.1. Tutorial¶
To use H-wave, you need to prepare the input files:
parameter file to set calculation conditions,
definition files of the Hamiltonian,
specifications to output the results,
before performing calculations.
In the following, we will provide a tutorial
using a sample in docs/tutorial/Hubbard/UHFr directory.
The interaction definition files can be generated using StdFace library.
See Generation of interaction files using StdFace library section for the details.
2.1.1. Create a parameter file¶
The parameter file contains information to control inputs and outputs of the program.
An example is given in the directory docs/tutorial/Hubbard/UHFr by the name input.toml.
The content of the file will be as follows:
[log]
print_level = 1
print_step = 20
[mode]
mode = "UHFr"
[mode.param]
Nsite = 8
2Sz = 0
Ncond = 8
IterationMax = 1000
EPS = 8
RndSeed = 123456789
T = 0.0
[file]
[file.input]
path_to_input = ""
OneBodyG = "greenone.def"
[file.input.interaction]
Trans = "trans.def"
CoulombIntra = "coulombintra.def"
[file.output]
path_to_output = "output"
energy = "energy.dat"
eigen = "eigen"
green = "green.dat"
The parameter file is described in TOML format.
In the log section, print_level specifies the level of the standard output, and print_step specifies the number of steps between printing logs.
In the mode section, the calculation mode and the basic parameters are specified.
In the file.input section, path_to_input specifies the directory in which input files are located, OneBodyG specifies the definition file of the one-body Green’s function to output, and Initial specifies the initial configuration.
If OneBodyG is missing, the Green’s function will not be exported.
When Initial is not specified, a random configuration will be generated for the initial state.
In the file.input.interaction section, the input files to define Hamiltonian are specified.
In the file.output section, path_to_output specifies the directory to which the results will be written. energy specifies the filename for the energy, eigen specifies the filename for the eigenvalues and eigenvectors of the Hamiltonian, and green specifies the filename for the one-body Green’s function.
If these keywords are missing, the corresponding results will not be exported.
See Parameter file section for the details.
2.1.2. Create definition files for Hamiltonian¶
Next, we will create input files that define the Hamiltonian.
Transfer term¶
The input file associated with a keyword Trans (trans.def in this tutorial)
provides definitions of Hamltonian for Transfer term of the electron system:
The content of the file is as follows:
========================
NTransfer 64
========================
========i_j_s_tijs======
========================
4 0 0 0 1.000000000000000 0.000000000000000
0 0 4 0 1.000000000000000 -0.000000000000000
4 1 0 1 1.000000000000000 0.000000000000000
0 1 4 1 1.000000000000000 -0.000000000000000
2 0 0 0 1.000000000000000 0.000000000000000
0 0 2 0 1.000000000000000 -0.000000000000000
2 1 0 1 1.000000000000000 0.000000000000000
0 1 2 1 1.000000000000000 -0.000000000000000
...
See Trans file for the details.
Two-body interaction term¶
In this tutorial, we consider a two-body interaction Hamiltonian of the electron system of the form:
The definition is given in the file associated with the keyword CoulombIntra
(coulombintra.def in the present case).
The content of the file is as follows:
=============================================
NCoulombIntra 8
=============================================
================== CoulombIntra ================
=============================================
0 8.000000000000000
1 8.000000000000000
2 8.000000000000000
3 8.000000000000000
4 8.000000000000000
...
There are a number of keywords provided to concicely describe the Hamiltonian,
besides CoulombIntra.
See sections InterAll file - PairLift file for the details.
2.1.3. Specify output components¶
Next, we will provide the files that describe the output components.
Setting indices of one-body Green’s functions¶
A file associated with the keyword OneBodyG (greenone.def in this tutorial) specifies
the indices of one-body Green’s functions to be calculated
\(\langle c_{i\sigma_1}^{\dagger}c_{j\sigma_2} \rangle\).
The content of the file will be as follows:
===============================
NCisAjs 16
===============================
======== Green functions ======
===============================
0 0 0 0
0 0 1 0
0 0 2 0
0 0 3 0
0 0 4 0
...
See OneBodyG file for the details of the file format to specify indices of the one-body Green’s functions.
2.1.4. Run¶
All the input files have been created, and we are ready to run the program.
Type in the command with the parameter file (input.toml in this tutorial) as an argument:
$ hwave input.toml
The calculation is launched, and the logs will be shown as follows:
2022-12-01 09:37:30,114 INFO qlms: Read def files
2022-12-01 09:37:30,116 INFO qlms: Get Hamiltonian information
2022-12-01 09:37:30,116 INFO qlms: Get Green function information
2022-12-01 09:37:30,116 INFO qlms.uhfr: Show input parameters
Nsite : 8
Ncond : 8
2Sz : 0
Mix : 0.5
EPS : 1e-08
IterationMax : 1000
RndSeed : 123456789
T : 0.0
ene_cutoff : 100.0
threshold : 1e-12
2022-12-01 09:37:30,117 INFO qlms: Start UHF calculation
2022-12-01 09:37:30,117 INFO qlms.uhfr: Set Initial Green's functions
2022-12-01 09:37:30,117 INFO qlms.uhfr: Initialize green function by random numbers
2022-12-01 09:37:30,117 INFO qlms.uhfr: Start UHFr calculations
2022-12-01 09:37:30,117 INFO qlms.uhfr: step, rest, energy, NCond, Sz
2022-12-01 09:37:30,119 INFO qlms.uhfr: 0, 0.022144468, -27.16081+0j, 8, -7.425e-16
2022-12-01 09:37:30,134 INFO qlms.uhfr: 20, 1.2083848e-05, -3.399532+0j, 8, -1.055e-15
2022-12-01 09:37:30,145 INFO qlms.uhfr: UHFr calculation is succeeded: rest=5.7552848630056134e-09, eps=1e-08.
2022-12-01 09:37:30,145 INFO qlms: Save calculation results.
2022-12-01 09:37:30,146 INFO qlms: All procedures are finished.
--------------------------------------------------------------------------------
Statistics
function : total elapsed : average elapsed : ncalls
--------------------------------------------------------------------------------
hwave.solver.uhfr.__init__ : 0.357 msec : 0.357 msec : 1
hwave.solver.uhfr._initial_G : 0.090 msec : 0.090 msec : 1
hwave.solver.uhfr._makeham_const : 0.839 msec : 0.839 msec : 1
hwave.solver.uhfr._makeham_mat : 0.309 msec : 0.309 msec : 1
hwave.solver.uhfr._makeham : 6.001 msec : 0.176 msec : 34
hwave.solver.uhfr._diag : 2.468 msec : 0.073 msec : 34
hwave.solver.uhfr._green : 3.107 msec : 0.091 msec : 34
hwave.solver.uhfr._calc_energy : 1.990 msec : 0.059 msec : 34
hwave.solver.uhfr._calc_phys : 12.929 msec : 0.380 msec : 34
hwave.solver.uhfr.solve : 28.290 msec : 28.290 msec : 1
hwave.solver.uhfr.save_results : 0.852 msec : 0.852 msec : 1
--------------------------------------------------------------------------------
The log messages on reading the input files are presented, followed by the information
on the process of UHF calculations.
The results are written in the output directory, according to the settings in file.output section of the input toml file:
energy.dat for the eigenvalues,
spin-up_eigen.npz and spin-down_eigen.npz for the eigenvectors, and
green.dat for the one-body Green’s functions.
See Output files for UHFr section for the details of the output files.
