5.2. Input file for tenes

• File format is TOML format.

• The input file has five sections: parameter, lattice, evolution, observable, correlation

  • In the future we will be able to split it by specifying the file name.

5.2.1. parameter section

Various parameters such as the number of updates are specified in this section. Only the parameters in this section have default values. This section has five sub sections, tensor, simple_update, full_update, ctm, random.

parameter.tensor

Name	Description	Type	Default
D	The virtual bond dimensions of the central tensor	Integer	2
CHI	The virtual bond dimensions of the angular transfer matrix	Integer	4
save_dir	Directory to write optimized tensors	Str	‘”“’
load_dir	Directory to read initial tensor	Str	‘”“’

• save_dir - Store optimized tensors below this directory. - When it is empty, the tensors are not saved.

• load_dir - Read various tensors from below this directory. - Must be same degree of parallelism as when saved. - Not read if it is empty.

parameter.simple_update

Name	Description	Type	Default
num_step	Number of simple updates	Integer	0
lambda_cutoff	cutoff of the mean field to be considered zero in the simple update	Real	1e-12

parameter.full_update

Name	Description	Type	Default
num_step	Number of full updates	Integer	0
env_cutoff	Cutoff of singular values to be considered as zero when computing environment through full updates	Real	1e-12
inverse_precision	Cutoff of singular values to be considered as zero when computing the pseudoinverse matrix with full update	Real	1e-12
convergence_epsilon	Convergence criteria for truncation optimization with full update	Real	1e-12
iteration_max	Maximum iteration number for truncation optimization on full updates	Integer	1000
gauge_fix	Whether the tensor gauge is fixed	Boolean	true
fastfullupdate	Whether the Fast full update is adopted	Boolean	true

parameter.ctm

Name	Description	Type	Default
projector_cutoff	Cutoff of singular values to be considered as zero when computing CTM projectors	Real	1e-12
convergence_epsilon	CTM convergence criteria	Real	1e-10
iteration_max	Maximum iteration number of convergence for CTM	Integer	100
projector_corner	Whether to use only the 1/4 corner tensor in the CTM projector calculation	Boolean	true
use_rsvd	Whether to replace SVD with Random SVD	Boolean	false
rsvd_oversampling_factor	Ratio of the number of the oversampled elements to that of the obtained elements in the Random SVD method	Real	2.0

parameter.random

Name	Description	Type	Default
seed	Seed of the pseudo-random number generator used to initialize the tensor	Integer	11

Each MPI process has the own seed as seed plus the process ID (MPI rank).

Example

[parameter]
[parameter.tensor]
D  = 4     # tensor_dim
CHI  = 16  # env_dim

[parameter.simple_update]
num_step = 1000

[parameter.full_update]
num_step = 1

[parameter.ctm]
iteration_max = 5

5.2.2. lattice section

Specify the unit cell information. Unit cell has a shape of a rectangular with the size of Lx times Ly.

Name	Description	Type
L_sub	Unit cell size	An integer or a list of integer

When a list of two integers is passed as L_sub, the first element gives the value of Lx and the second one does Ly. If L_sub is an integer, Both Lx and Ly will have the same value. A list of three or more elements causes an error.

Sites in a unit cell are indexed starting from 0. These are arranged in order from the x direction.

Sites in a unit cell of L_sub = [2,3] are arranged as follows:

y
^     4 5
|     2 3
.->x  0 1

Information of bonds is given in the evolution and the observable sections.

5.2.3. evolution section

Define the imaginary time evolution opetrators used in simple and full updates.

Name	Description	Type
matrix	Matrix representation about the imaginary time evolution opetrators	A list of string
simple_update	The order of the bonds that act on the index of the imaginary time evolution operator in simple update	A list of string
full_update	The order of the bonds that act on the index of the imaginary time evolution operator in full update	A list of string

matrix

• One matrix is defined by a list of string.

• Columns are separated by one or more blanks, and rows are separated by one or more newlines.

• The order defined corresponds exactly to the number of the matrix. This order numbers are used to specify simple_update and full_update (0-origin).

simple_update and full_update

• One row represents one operator action.

• Each line consists of four fields: int int string int.

  1. A site to which bond connects

  2. A site to which bond connects

  3. Horizontal (h) or Vertical (v)

  4. Operator number (0-origin)

Example

[evolution]
simple_update = """
0 1 h 0
3 2 h 0
2 3 h 0
1 0 h 0
0 2 v 0
3 1 v 0
2 0 v 0
1 3 v 0
"""

full_update = """
0 1 h 0
3 2 h 0
2 3 h 0
1 0 h 0
0 2 v 0
3 1 v 0
2 0 v 0
1 3 v 0
"""

matrix = [
"""
0.9975031223974601 0.0 0.0 0.0
0.0 1.0025156589209967 -0.005012536523536887 0.0
0.0 -0.005012536523536888 1.0025156589209967 0.0
0.0 0.0 0.0 0.9975031223974601
"""
]

5.2.4. observable section

In this section, the information about physical quantities to be observed is specified.

Name	Description	Type
local_operator	Site opertor (ex. Sz)	A list of string
hamiltonian	Bond hamiltonian	A list of string
hamiltonian_bonds	Type of bond Hamiltonian and the set of bonds that act	string

local_operator, hamiltonian

Same as evolution.matrix . The order you define corresponds exactly to the index of the operator Hamiltonian.

hamiltonian_bonds

Same as evolution.simple_update .

Example

[observable]
local_operator = [
"""
  0.5  0.0
  0.0 -0.5
""",
"""
  0.0 0.5
  0.5 0.0
""",
]

hamiltonian_bonds = """
0 1 h 0
3 2 h 0
2 3 h 0
1 0 h 0
0 2 v 0
3 1 v 0
2 0 v 0
1 3 v 0
"""

hamiltonian = [
"""
  0.25   0.0    0.0     0.0
  0.0   -0.25   0.5     0.0
  0.0    0.5   -0.25    0.0
  0.0    0.0    0.0     0.25
""",
]

5.2.5. correlation section

In the following, the parameters about the correlation function \(C = \langle A(0)B(r) \rangle\) is described.

Name	Description	Type
r_max	Maximum distance \(r\) of the correlation function	Integer
operators	Numbers of operators A and B that measure correlation functions	A list for Integer

The operators defined in the observable section are used.

Example

[correlation]
r_max = 5
operators = [[0,0], [0,1], [1,1]]