5.5. Output files

Output files are generated in the output directry.

5.5.1. For all modes

parameters.dat

Paramters in the parameter and lattice sections defined in the input file are outputted.

Example:

simple_num_step = [10]
simple_tau = [0.01]
simple_inverse_lambda_cutoff = 1e-12
simple_gauge_fix = 0
simple_gauge_maxiter = 100
simple_gauge_convergence_epsilon = 0.01

full_num_step = [0]
full_inverse_projector_cutoff = 1e-12
full_inverse_precision = 1e-12
full_convergence_epsilon = 1e-06
full_iteration_max = 100
full_gauge_fix = true
full_fastfullupdate = true

ctm_dimension = 10
ctm_inverse_projector_cutoff = 1e-12
ctm_convergence_epsilon = 1e-06
ctm_iteration_max = 10
ctm_projector_corner = true
use_rsvd = false
rsvd_oversampling_factor = 2
meanfield_env = true

mode = ground state
simple
Lcor = 0
seed = 11
is_real = 0
iszero_tol = 0
measure = 1
tensor_load_dir =
tensor_save_dir = save_tensor
outdir = output

Lsub = [ 2 , 2 ]
skew = 0

start_datetime =  2023-06-08T16:41:50+09:00

time.dat

The calculation time is outputted.

Example:

time simple update = 1.64429
time full update   = 0
time environmnent  = 0.741858
time observable    = 0.104487

5.5.2. For ground state calculation mode

density.dat

The expectation value per site of each observable is outputted. When the name of the operator (name) is an empty, the index of the operator is written. Energy means the summation of site hamiltonian and bond hamiltonian.

Example:

Energy           = -5.00499902760266346e-01  0.00000000000000000e+00
site hamiltonian = -4.99999945662006270e-04  0.00000000000000000e+00
Sz               =  4.99999945662006284e-01  0.00000000000000000e+00
Sx               =  9.24214061616647275e-05  0.00000000000000000e+00
Sy               = -2.34065881671767322e-06  0.00000000000000000e+00
bond hamiltonian = -4.99999902814604325e-01  2.22346094146706503e-21
SzSz             =  4.99999902814604380e-01 -1.80051315353166456e-21
SxSx             =  1.12631053560300631e-05  6.08792260271591701e-21
SySy             = -1.12817627661272438e-05  4.76468712680822333e-21

onesite_obs.dat

  • The expected values of the site operator \(\langle\hat{A}^\alpha_i\rangle = \langle\Psi | \hat{A}^\alpha_i | \Psi \rangle / \langle\Psi | \Psi \rangle\) are outputted.

  • Each row consists of four columns.

    1. Index of the operator \(\alpha\)

    2. Index of the sites \(i\)

    3. Real part of the expected value \(\mathrm{Re}\langle\hat{A}^\alpha_i\rangle\)

    4. Imag part of the expected value \(\mathrm{Im}\langle\hat{A}^\alpha_i\rangle\)

  • In addition, norm of the wave function \(\langle \Psi | \Psi \rangle\) is outputted as an operator with index of -1.

    • If the imaginary part is finite, something is wrong. A typical cause is that the bond dimension of the CTM is too small.

Example:

# The meaning of each column is the following:
# $1: op_group
# $2: site_index
# $3: real
# $4: imag
# The names of op_group are the following:
# 0: site hamiltonian
# 1: Sz
# 2: Sx
# 3: Sy
# -1: norm

0 0 -4.99999945520001373e-04 0.00000000000000000e+00
0 1 -4.99999967900088089e-04 0.00000000000000000e+00
0 2 -4.99999894622883147e-04 0.00000000000000000e+00
0 3 -4.99999974605052581e-04 0.00000000000000000e+00
1 0 4.99999945520001376e-01 0.00000000000000000e+00
1 1 4.99999967900088049e-01 0.00000000000000000e+00
1 2 4.99999894622883134e-01 0.00000000000000000e+00
1 3 4.99999974605052522e-01 0.00000000000000000e+00
   ... Skipped ...
-1 3 1.00000000000000044e+00 0.00000000000000000e+00

twosite_obs.dat

  • Expectation values for two-site operations are outputted.

  • Each row consists of six columns.

    1. Index of the two-site operator

    2. Index of the source site

    3. x coordinate of the target site from the source site

    4. y coordinate of the target site from the source site

    5. Real part of the expected value

    6. Imaginary part of the expected value

  • In addition, norm of the wave function \(\langle \Psi | \Psi \rangle\) is outputted as an operator with index of -1.

    • If the imaginary part is finite, something is wrong. A typical cause is that the bond dimension of the CTM is too small.

Example:

# The meaning of each column is the following:
# $1: op_group
# $2: source_site
# $3: dx
# $4: dy
# $5: real
# $6: imag
# The names of op_group are the following:
# 0: bond hamiltonian
# 1: SzSz
# 2: SxSx
# 3: SySy
# -1: norm

0 0 0 1 -2.49999925774909121e-01 3.38316768671362694e-21
0 0 1 0 -2.49999967989907063e-01 4.24343236807659553e-22
0 1 0 1 -2.49999972903562101e-01 -2.06825262200104597e-25
0 1 1 0 -2.49999957625646446e-01 2.06789370628128221e-24
0 2 0 1 -2.49999931343147630e-01 3.11801499860976615e-28
0 2 1 0 -2.49999939447834718e-01 1.65429596395607220e-24
   ... Skipped ...
-1 3 1 0 1.00000000000000067e+00 0.00000000000000000e+00

multisite_obs_#.dat

  • Expectation values for multi-site operations are outputted.

  • # in the filename is replaced by the number of sites in the operator, \(N\).

  • Each row consists of \(4+2(N-1)\) columns.

  • The first column is the index of the operator.

  • The second column is the index of the site, which is the origin of the coordinate.

  • The following columns are the relative coordinates of the other sites.

  • The last two columns are the real and imaginary parts of the expected value.

correlation.dat

  • Correlation functions \(C^{\alpha \beta}_i(x,y) \equiv \langle \hat{A}^\alpha(x_i,y_i) \hat{A}^\beta(x_i+x,y_i+y) \rangle\) are outputted.

  • Each row consists of seven columns.

    1. Index of the left operator \(\alpha\)

    2. Index of the left site \(i\)

    3. Index of the right operator \(\beta\)

    4. x coordinate of the right site \(x\)

    5. y coordinate of the right site \(y\)

    6. Real part \(\mathrm{Re}C\)

    7. Imaginary part \(\mathrm{Im}C\)

Example:

# $1: left_op
# $2: left_site
# $3: right_op
# $4: right_dx
# $5: right_dy
# $6: real
# $7: imag

0 0 0 1 0 -1.71759992763061836e-01 1.36428299157186382e-14
0 0 0 2 0 1.43751794649139675e-01 -1.14110668277268192e-14
0 0 0 3 0 -1.42375391377041444e-01 1.14103263451826963e-14
0 0 0 4 0 1.41835919840103741e-01 -1.11365361507372103e-14
0 0 0 5 0 -1.41783912096811515e-01 1.12856813523671142e-14
0 0 0 0 1 -1.72711348845767942e-01 1.40873628493918905e-14
0 0 0 0 2 1.43814797743900907e-01 -1.17958665742991377e-14
0 0 0 0 3 -1.42415176172922653e-01 1.22109610917000360e-14
0 0 0 0 4 1.41838862178711583e-01 -1.19321507524565005e-14
0 0 0 0 5 -1.41792935491960648e-01 1.23094733264734764e-14
1 0 1 1 0 -7.95389427681298805e-02 6.15901595234210079e-15
1 0 1 2 0 2.01916094009441903e-02 -1.27162373457160362e-15
... Skipped ...
2 3 2 0 5 -1.41888376278899312e-03 -2.38672137694415560e-16

correlation_length.dat

The correlation length \(\xi\) is outputted. Each row consists of 3+n columns.

  1. Direction (0: x, 1: y)

  2. When direction is 0 it is \(y\) coodinate, and otherwise \(x\) coordinate

  3. Correlation length \(\xi = 1/e_1\)

The 4th and the subsequent columns show the logarithm of the absolute value of the eigenvalues of the transfer matrix, \(e_i = -\log\left|\lambda_i/\lambda_0\right|\) (\(i>0\)). This information may be used to estimate the bond dimension dependence of the correlation length. See PRX 8, 041033 (2018) and PRX 8, 031030 (2018) for more information.

Example:

# The meaning of each column is the following:
# $1: direction 0: +x, 1: +y
# $2: y (dir=0) or x (dir=1) coorinates
# $3: correlation length xi = 1/e_1
# $4-: eigenvalues e_i = -log|t_i/t_0|
#      where i > 0 and t_i is i-th largest eigenvalue of T

0 0 2.18785686529154477e-01 4.57068291744370647e+00 4.57068291744370647e+00 4.88102462824739991e+00
0 1 2.20658864940629751e-01 4.53188228022952533e+00 4.53188228022952533e+00 4.56359469233104953e+00
1 0 2.23312072254469030e-01 4.47803824443704013e+00 4.47803824443704013e+00 6.03413555039678595e+00
1 1 2.00830966658579996e-01 4.97931178960083720e+00 4.97931178960083720e+00 5.08813099309339911e+00

5.5.3. For time evolution mode

TE_density.dat

The expectation value per site of each obesrvable is outputted. Each row consists of four columns.

  1. Time \(t\)

  2. Operator ID \(\alpha\)

  3. Real part of the expected value \(\mathrm{Re}\langle\hat{A}^\alpha_i\rangle\)

  4. Imag part of the expected value \(\mathrm{Im}\langle\hat{A}^\alpha_i\rangle\)

Example:

# The meaning of each column is the following:
# $1: time
# $2: observable ID
# $3: real
# $4: imag
# The meaning of observable IDs are the following:
# 0: Energy
# 1: site hamiltonian
# 2: Sz
# 3: Sx
# 4: Sy
# 5: bond hamiltonian
# 6: SzSz
# 7: SxSx
# 8: SySy

0.00000000000000000e+00 0 -5.00684745572451129e-01  0.00000000000000000e+00
0.00000000000000000e+00 1 -6.84842757985213292e-04  0.00000000000000000e+00
0.00000000000000000e+00 2  4.99999945661913914e-01  0.00000000000000000e+00
0.00000000000000000e+00 3  9.24214061616496842e-05  0.00000000000000000e+00
   ... Skipped ...
4.99999999999993783e+00 8  2.54571641402435656e-01  3.25677610112348483e-17

TE_onesite_obs.dat

The expected values of the site operators \(\langle\hat{A}^\alpha_i\rangle = \langle\Psi | \hat{A}^\alpha_i | \Psi \rangle / \langle\Psi | \Psi \rangle\) are outputted. Each row consists of five columns.

  1. Time \(t\)

  2. Index of the operator \(\alpha\)

  3. Index of the sites \(i\)

  4. Real part of the expected value \(\mathrm{Re}\langle\hat{A}^\alpha_i\rangle\)

  5. Imag part of the expected value \(\mathrm{Im}\langle\hat{A}^\alpha_i\rangle\)

  • In addition, norm of the wave function \(\langle \Psi | \Psi \rangle\) is outputted as an operator with index of -1.

    • If the imaginary part is finite, something is wrong. A typical cause is that the bond dimension of the CTM is too small.

Example:

# The meaning of each column is the following:
# $1: time
# $2: op_group
# $3: site_index
# $4: real
# $5: imag
# The names of op_group are the following:
# 0: site hamiltonian
# 1: Sz
# 2: Sx
# 3: Sy
# -1: norm

0.00000000000000000e+00 0 0 -6.43318936197596913e-04 0.00000000000000000e+00
0.00000000000000000e+00 0 1 -6.73418200262321655e-04 0.00000000000000000e+00
0.00000000000000000e+00 0 2 -9.89240026254938282e-04 0.00000000000000000e+00
0.00000000000000000e+00 0 3 -4.33393869225996210e-04 0.00000000000000000e+00
0.00000000000000000e+00 1 0 4.99999945519898625e-01 0.00000000000000000e+00
0.00000000000000000e+00 1 1 4.99999967900020936e-01 0.00000000000000000e+00
0.00000000000000000e+00 1 2 4.99999894622765451e-01 0.00000000000000000e+00
   ... Skipped ...
4.99999999999993783e+00 -1 3 9.99999999999999667e-01 0.00000000000000000e+00

TE_twosite_obs.dat

  • Expectation values for two-site operations are outputted.

  • Each row consists of six columns.

    1. Time \(t\)

    2. Index of the two-site operator

    3. Index of the source site

    4. x coordinate of the target site from the source site

    5. y coordinate of the target site from the source site

    6. Real part of the expected value

    7. Imaginary part of the expected value

  • In addition, norm of the wave function \(\langle \Psi | \Psi \rangle\) is outputted as an operator with index of -1.

    • If the imaginary part is finite, something is wrong. A typical cause is that the bond dimension of the CTM is too small.

Example:

# The meaning of each column is the following:
# $1: time
# $2: op_group
# $3: source_site
# $4: dx
# $5: dy
# $6: real
# $7: imag
# The names of op_group are the following:
# 0: bond hamiltonian
# 1: SzSz
# 2: SxSx
# 3: SySy
# -1: norm

0.00000000000000000e+00 0 0 0 1 -2.49999925774803150e-01 -1.01660465821037727e-20
0.00000000000000000e+00 0 0 1 0 -2.49999967989888300e-01 4.23516895582898471e-22
0.00000000000000000e+00 0 1 0 1 -2.49999972903488521e-01 -6.20403358955599675e-25
0.00000000000000000e+00 0 1 1 0 -2.49999957625561042e-01 4.13590865617858526e-25
0.00000000000000000e+00 0 2 0 1 -2.49999931343070220e-01 8.27316466562544801e-25
   ... Skipped ...
4.99999999999993783e+00 -1 3 1 0 9.99999999999999445e-01 1.38777878078144568e-17

TE_multisite_obs_#.dat

  • Expectation values for multi-site operations are outputted.

  • # in the filename is replaced by the number of sites in the operator, \(N\).

  • Each row consists of \(5+2(N-1)\) columns.

  • The first column is the time \(t\).

  • The second column is the index of the operator.

  • The third column is the index of the site, which is the origin of the coordinate.

  • The following columns are the relative coordinates of the other sites.

  • The last two columns are the real and imaginary parts of the expected value.

TE_correlation.dat

  • Correlation functions \(C^{\alpha \beta}_i(x,y) \equiv \langle \hat{A}^\alpha(x_i,y_i) \hat{A}^\beta(x_i+x,y_i+y) \rangle\) are outputted.

  • Each row consists of eight columns.

    1. Time \(t\)

    2. Index of the left operator \(\alpha\)

    3. Index of the left site \(i\)

    4. Index of the right operator \(\beta\)

    5. x coordinate of the right site \(x\)

    6. y coordinate of the right site \(y\)

    7. Real part \(\mathrm{Re}C\)

    8. Imaginary part \(\mathrm{Im}C\)

Example:

# The meaning of each column is the following:
# $1: time
# $2: left_op
# $3: left_site
# $4: right_op
# $5: right_dx
# $6: right_dy
# $7: real
# $8: imag
# The names of operators are the following:
# 0: site hamiltonian
# 1: Sz
# 2: Sx
# 3: Sy

0.00000000000000000e+00 0 0 0 1 0 1.83422488349707711e-04 1.90382762094233524e-20
0.00000000000000000e+00 0 0 0 2 0 8.30943360551218668e-07 -4.19695835411528090e-23
0.00000000000000000e+00 0 0 0 3 0 4.12158436385765748e-07 -1.04903226091485958e-23
0.00000000000000000e+00 0 0 0 4 0 4.13819451426396547e-07 1.74438421668770658e-23
0.00000000000000000e+00 0 0 0 5 0 4.33224506806043380e-07 -8.71850465073480394e-24
   ... Skipped ...
4.99999999999993783e+00 2 3 2 0 5 3.96301355731331212e-02 -1.37659660157453792e-18

TE_correlation_length.dat

The correlation length \(\xi\) is outputted. Each row consists of 4+n columns.

  1. Time \(t\)

  2. Direction (0: x, 1: y)

  3. When direction is 0 it is \(y\) coodinate, and otherwise \(x\) coordinate

  4. Correlation length \(\xi = 1/e_1\)

The 5th and the subsequent columns show the logarithm of the absolute value of the eigenvalues of the transfer matrix, \(e_i = -\log\left|\lambda_i/\lambda_0\right|\) (\(i>0\)). This information may be used to estimate the bond dimension dependence of the correlation length. See PRX 8, 041033 (2018) and PRX 8, 031030 (2018) for more information.

Example:

# The meaning of each column is the following:
# $1: time
# $2: direction 0: +x, 1: +y
# $3: y (dir=0) or x (dir=1) coorinates
# $4: correlation length xi = 1/e_1
# $5-: eigenvalues e_i = -log|t_i/t_0|
#      where i > 0 and t_i is i-th largest eigenvalue of T

0.00000000000000000e+00 0 0 2.18785686529220424e-01 4.57068291744232891e+00 4.57068291744232891e+00 4.88102462824919758e+00
0.00000000000000000e+00 0 1 2.20658864940612931e-01 4.53188228022987083e+00 4.53188228022987083e+00 4.56359469232955917e+00
0.00000000000000000e+00 1 0 2.23312072254560540e-01 4.47803824443520515e+00 4.47803824443520515e+00 6.03413555040836602e+00
0.00000000000000000e+00 1 1 2.00830966658709920e-01 4.97931178959761578e+00 4.97931178959761667e+00 5.08813099310449513e+00
9.99999999999999917e-02 0 0 2.02379048126702904e-01 4.94122296382149528e+00 4.94122296382149617e+00 6.74309974506451315e+00
9.99999999999999917e-02 0 1 2.20416567580991346e-01 4.53686404327366777e+00 4.53686404327366777e+00 6.18101616573088020e+00
9.99999999999999917e-02 1 0 2.12137154053103655e-01 4.71393143960851368e+00 4.71393143960851368e+00 7.17220113786375002e+00
9.99999999999999917e-02 1 1 1.90367314703518503e-01 5.25300260476656966e+00 5.25300260476656966e+00 7.61893825410630487e+00
2.00000000000000039e-01 0 0 1.96835348300227503e-01 5.08038829730281805e+00 5.08038829730281805e+00 7.35176717846311778e+00
2.00000000000000039e-01 0 1 2.02355022722768896e-01 4.94180963014702801e+00 4.94180963014702801e+00 6.57691315725687975e+00
2.00000000000000039e-01 1 0 2.05314677188187883e-01 4.87057239986509760e+00 4.87057239986509760e+00 7.90951918842309798e+00
2.00000000000000039e-01 1 1 1.63323696507474692e-01 6.12281023136305169e+00 6.12281023136305169e+00 7.83104916294462416e+00
   ... Skipped ...
4.99999999999993783e+00 1 1 4.61585992965019176e-01 2.16644355600232430e+00 2.16644355600232430e+00 2.29497956495965427e+00

5.5.4. For finite temperature calculation mode

The formats of the files are the same as those in the real time evolution mode. The only difference is that the file name starts with FT_ instead of TE_, and the first column is the inverse temperature \(\beta = 1/T\) instead of the time \(t\).