DMRGEngine¶
full name: tenpy.algorithms.dmrg.DMRGEngine
parent module:
tenpy.algorithms.dmrg
type: class
Inheritance Diagram
Methods
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Initialize self. |
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Diagonalize the effective Hamiltonian represented by self. |
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Perform N_sweeps sweeps without optimization to update the environment. |
Define the schedule of the sweep. |
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(Re-)initialize the environment. |
Create new instance of self.EffectiveH at self.i0 and set it to self.eff_H. |
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Cleanup the effects of a mixer. |
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Plot |
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Plot |
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Perform post-update actions. |
Prepare everything algorithm-specific to perform a local update. |
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Reset the statistics, useful if you want to start a new sweep run. |
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Run the DMRG simulation to find the ground state. |
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One ‘sweep’ of a the algorithm. |
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Perform algorithm-specific local update. |
Class Attributes and Properties
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-
class
tenpy.algorithms.dmrg.
DMRGEngine
(psi, model, options)[source]¶ Bases:
tenpy.algorithms.mps_common.Sweep
DMRG base class.’Engine’ for the DMRG algorithm.
This engine is implemented as a subclass of
Sweep
. It contains all methods that are generic betweenSingleSiteDMRGEngine
andTwoSiteDMRGEngine
.Deprecated since version 0.5.0: Renamed parameter/attribute DMRG_params to
options
.Options
-
config
DMRGEngine
¶ option summary chi_list in DMRGEngine.reset_stats
A dictionary to gradually increase the `chi_max` parameter of [...]
Whether to combine legs into pipes. This combines the virtual and [...]
diag_method in DMRGEngine.run
Method to be used for diagonalzation, default ``'default'``. [...]
E_tol_max in DMRGEngine.run
See `E_tol_to_trunc`
E_tol_min in DMRGEngine.run
See `E_tol_to_trunc`
E_tol_to_trunc in DMRGEngine.run
It's reasonable to choose the Lanczos convergence criteria [...]
init_env_data (from Sweep) in DMRGEngine.init_env
Dictionary as returned by ``self.env.get_initialization_data()`` from [...]
lanczos_params (from Sweep) in Sweep
Lanczos parameters as described in [...]
max_E_err in DMRGEngine.run
Convergence if the change of the energy in each step [...]
max_hours in DMRGEngine.run
If the DMRG took longer (measured in wall-clock time), [...]
max_N_for_ED in DMRGEngine.diag
Maximum matrix dimension of the effective hamiltonian [...]
max_S_err in DMRGEngine.run
Convergence if the relative change of the entropy in each step [...]
max_sweeps in DMRGEngine.run
Maximum number of sweeps to be performed.
min_sweeps in DMRGEngine.run
Minimum number of sweeps to be performed. [...]
N_sweeps_check in DMRGEngine.run
Number of sweeps to perform between checking convergence [...]
norm_tol in DMRGEngine.run
After the DMRG run, update the environment with at most [...]
norm_tol_iter in DMRGEngine.run
Perform at most `norm_tol_iter`*`update_env` sweeps to [...]
orthogonal_to (from Sweep) in DMRGEngine.init_env
List of other matrix product states to orthogonalize against. [...]
P_tol_max in DMRGEngine.run
See `P_tol_to_trunc`
P_tol_min in DMRGEngine.run
See `P_tol_to_trunc`
P_tol_to_trunc in DMRGEngine.run
It's reasonable to choose the Lanczos convergence criteria [...]
Number of sweeps to be performed without optimization to update [...]
sweep_0 in DMRGEngine.reset_stats
The number of sweeps already performed. (Useful for re-start).
trunc_params (from Sweep) in Sweep
Truncation parameters as described in :cfg:config:`truncation`.
update_env in DMRGEngine.run
Number of sweeps without bond optimizaiton to update the [...]
Level of verbosity (i.e. how much status information to print); higher=more [...]
-
EffectiveH
¶ Class for the effective Hamiltonian, i.e., a subclass of
EffectiveH
. Has a length class attribute which specifies the number of sites updated at once (e.g., whether we do single-site vs. two-site DMRG).- Type
class type
-
chi_list
¶ -
- Type
dict |
None
-
eff_H
¶ Effective two-site Hamiltonian.
- Type
-
shelve
¶ If a simulation runs out of time (time.time() - start_time > max_seconds), the run will terminate with shelve = True.
- Type
-
update_stats
¶ A dictionary with detailed statistics of the convergence at local update-level. For each key in the following table, the dictionary contains a list where one value is added each time
DMRGEngine.update_bond()
is called.key
description
i0
An update was performed on sites
i0, i0+1
.age
The number of physical sites involved in the simulation.
E_total
The total energy before truncation.
N_lanczos
Dimension of the Krylov space used in the lanczos diagonalization.
time
Wallclock time evolved since
time0
(in seconds).ov_change
1. - abs(<theta_guess|theta_diag>)
, where|theta_guess>
is the initial guess for the wave function and|theta_diag>
is the untruncated wave function returned bydiag()
.- Type
-
sweep_stats
¶ A dictionary with detailed statistics at the sweep level. For each key in the following table, the dictionary contains a list where one value is added each time
Engine.sweep()
is called (withoptimize=True
).key
description
sweep
Number of sweeps (excluding environment sweeps) performed so far.
N_updates
Number of updates (including environment sweeps) performed so far.
E
The energy before truncation (as calculated by Lanczos).
S
Maximum entanglement entropy.
time
Wallclock time evolved since
time0
(in seconds).max_trunc_err
The maximum truncation error in the last sweep
max_E_trunc
Maximum change or Energy due to truncation in the last sweep.
max_chi
Maximum bond dimension used.
norm_err
Error of canonical form
np.linalg.norm(psi.norm_test())
.- Type
-
run
()[source]¶ Run the DMRG simulation to find the ground state.
- Returns
E (float) – The energy of the resulting ground state MPS.
psi (
MPS
) – The MPS representing the ground state after the simluation, i.e. just a reference topsi
.
Options
-
option
DMRGEngine
.
diag_method
: str¶ Method to be used for diagonalzation, default
'default'
. For possible arguments seeDMRGEngine.diag()
.
-
option
DMRGEngine
.
E_tol_to_trunc
: float¶ It’s reasonable to choose the Lanczos convergence criteria
'E_tol'
not many magnitudes lower than the current truncation error. Therefore, if E_tol_to_trunc is notNone
, we update E_tol of lanczos_params tomax_E_trunc*E_tol_to_trunc
, restricted to the interval [E_tol_min, E_tol_max], wheremax_E_trunc
is the maximal energy difference due to truncation right after each Lanczos optimization during the sweeps.
-
option
DMRGEngine
.
E_tol_max
: float¶ See E_tol_to_trunc
-
option
DMRGEngine
.
E_tol_min
: float¶ See E_tol_to_trunc
-
option
DMRGEngine
.
max_E_err
: float¶ Convergence if the change of the energy in each step satisfies
-Delta E / max(|E|, 1) < max_E_err
. Note that this is also satisfied ifDelta E > 0
, i.e., if the energy increases (due to truncation).
-
option
DMRGEngine
.
max_hours
: float¶ If the DMRG took longer (measured in wall-clock time), ‘shelve’ the simulation, i.e. stop and return with the flag
shelve=True
.
-
option
DMRGEngine
.
max_S_err
: float¶ Convergence if the relative change of the entropy in each step satisfies
|Delta S|/S < max_S_err
-
option
DMRGEngine
.
max_sweeps
: int¶ Maximum number of sweeps to be performed.
-
option
DMRGEngine
.
min_sweeps
: int¶ Minimum number of sweeps to be performed. Defaults to 1.5*N_sweeps_check.
-
option
DMRGEngine
.
N_sweeps_check
: int¶ Number of sweeps to perform between checking convergence criteria and giving a status update.
-
option
DMRGEngine
.
norm_tol
: float¶ After the DMRG run, update the environment with at most norm_tol_iter sweeps until
np.linalg.norm(psi.norm_err()) < norm_tol
.
-
option
DMRGEngine
.
norm_tol_iter
: float¶ Perform at most norm_tol_iter`*`update_env sweeps to converge the norm error below norm_tol. If the state is not converged after that, call
canonical_form()
instead.
-
option
DMRGEngine
.
P_tol_to_trunc
: float¶ It’s reasonable to choose the Lanczos convergence criteria
'P_tol'
not many magnitudes lower than the current truncation error. Therefore, if P_tol_to_trunc is notNone
, we update P_tol of lanczos_params tomax_trunc_err*P_tol_to_trunc
, restricted to the interval [P_tol_min, P_tol_max], wheremax_trunc_err
is the maximal truncation error (discarded weight of the Schmidt values) due to truncation right after each Lanczos optimization during the sweeps.
-
option
DMRGEngine
.
P_tol_max
: float¶ See P_tol_to_trunc
-
option
DMRGEngine
.
P_tol_min
: float¶ See P_tol_to_trunc
-
option
DMRGEngine
.
update_env
: int¶ Number of sweeps without bond optimizaiton to update the environment for infinite boundary conditions, performed every N_sweeps_check sweeps.
-
reset_stats
()[source]¶ Reset the statistics, useful if you want to start a new sweep run.
-
option
DMRGEngine
.
chi_list
: dict | None¶ A dictionary to gradually increase the chi_max parameter of trunc_params. The key defines starting from which sweep chi_max is set to the value, e.g.
{0: 50, 20: 100}
useschi_max=50
for the first 20 sweeps andchi_max=100
afterwards. Overwrites trunc_params[‘chi_list’]`. By default (None
) this feature is disabled.
-
option
DMRGEngine
.
sweep_0
: int¶ The number of sweeps already performed. (Useful for re-start).
-
option
-
post_update_local
(update_data)[source]¶ Perform post-update actions.
Compute truncation energy, remove LP/RP that are no longer needed and collect statistics.
- Parameters
update_data (dict) – What was returned by
update_local()
.
-
diag
(theta_guess)[source]¶ Diagonalize the effective Hamiltonian represented by self.
-
option
DMRGEngine
.
max_N_for_ED
: int¶ Maximum matrix dimension of the effective hamiltonian up to which the
'default'
diag_method uses ED instead of Lanczos.
-
option
DMRGEngine
.
diag_method
: str¶ One of the folloing strings:
- ‘default’
Same as
'lanczos'
for large bond dimensions, but if the total dimension of the effective Hamiltonian does not exceed the DMRG parameter'max_N_for_ED'
it uses'ED_block'
.- ‘lanczos’
lanczos()
Default, the Lanczos implementation in TeNPy.- ‘arpack’
lanczos_arpack()
Based onscipy.linalg.sparse.eigsh()
. Slower than ‘lanczos’, since it needs to convert the npc arrays to numpy arrays during each matvec, and possibly does many more iterations.- ‘ED_block’
full_diag_effH()
Contract the effective Hamiltonian to a (large!) matrix and diagonalize the block in the charge sector of the initial state. Preserves the charge sector of the explicitly conserved charges. However, if you don’t preserve a charge explicitly, it can break it. For example if you use aSpinChain({'conserve': 'parity'})
, it could change the total “Sz”, but not the parity of ‘Sz’.- ‘ED_all’
full_diag_effH()
Contract the effective Hamiltonian to a (large!) matrix and diagonalize it completely. Allows to change the charge sector even for explicitly conserved charges. For example if you use aSpinChain({'conserve': 'Sz'})
, it can change the total “Sz”.
- Parameters
theta_guess (
Array
) – Initial guess for the ground state of the effective Hamiltonian.- Returns
E0 (float) – Energy of the found ground state.
theta (
Array
) – Ground state of the effective Hamiltonian.N (int) – Number of Lanczos iterations used.
-1
if unknown.ov_change (float) – Change in the wave function
1. - abs(<theta_guess|theta_diag>)
-
option
-
plot_update_stats
(axes, xaxis='time', yaxis='E', y_exact=None, **kwargs)[source]¶ Plot
update_stats
to display the convergence during the sweeps.- Parameters
axes (
matplotlib.axes.Axes
) – The axes to plot into. Defaults tomatplotlib.pyplot.gca()
xaxis (
'N_updates' | 'sweep'
| keys ofupdate_stats
) – Key ofupdate_stats
to be used for the x-axis of the plots.'N_updates'
is just enumerating the number of bond updates, and'sweep'
corresponds to the sweep number (including environment sweeps).yaxis (
'E'
| keys ofupdate_stats
) – Key ofupdate_stats
to be used for the y-axisof the plots. For ‘E’, use the energy (per site for infinite systems).y_exact (float) – Exact value for the quantity on the y-axis for comparison. If given, plot
abs((y-y_exact)/y_exact)
on a log-scale yaxis.**kwargs – Further keyword arguments given to
axes.plot(...)
.
-
plot_sweep_stats
(axes=None, xaxis='time', yaxis='E', y_exact=None, **kwargs)[source]¶ Plot
sweep_stats
to display the convergence with the sweeps.- Parameters
axes (
matplotlib.axes.Axes
) – The axes to plot into. Defaults tomatplotlib.pyplot.gca()
yaxis (xaxis,) – Key of
sweep_stats
to be used for the x-axis and y-axis of the plots.y_exact (float) – Exact value for the quantity on the y-axis for comparison. If given, plot
abs((y-y_exact)/y_exact)
on a log-scale yaxis.**kwargs – Further keyword arguments given to
axes.plot(...)
.
-
mixer_cleanup
()[source]¶ Cleanup the effects of a mixer.
A
sweep()
with an enabledMixer
leaves the MPS psi with 2D arrays in S. To recover the originial form, this function simply performs one sweep with disabled mixer.
-
sweep
(optimize=True, meas_E_trunc=False)[source]¶ One ‘sweep’ of a the algorithm.
Iteratate over the bond which is optimized, to the right and then back to the left to the starting point.
- Parameters
- Returns
max_trunc_err (float) – Maximal truncation error introduced.
max_E_trunc (
None
| float) –None
if meas_E_trunc is False, else the maximal change of the energy due to the truncation.
-
environment_sweeps
(N_sweeps)[source]¶ Perform N_sweeps sweeps without optimization to update the environment.
- Parameters
N_sweeps (int) – Number of sweeps to run without optimization
-
get_sweep_schedule
()[source]¶ Define the schedule of the sweep.
One ‘sweep’ is a full sequence from the leftmost site to the right and back. Only those LP and RP that can be used later should be updated.
- Returns
schedule – Schedule for the sweep. Each entry is
(i0, move_right, (update_LP, update_RP))
, where i0 is the leftmost of theself.EffectiveH.length
sites to be updated inupdate_local()
, move_right indicates whether the next i0 in the schedule is rigth (True) of the current one, and update_LP, update_RP indicate whether it is necessary to update the LP and RP. The latter are chosen such that the environment is growing for infinite systems, but we only keep the minimal number of environment tensors in memory.- Return type
-
init_env
(model=None)[source]¶ (Re-)initialize the environment.
This function is useful to (re-)start a Sweep with a slightly different model or different (engine) parameters. Note that we assume that we still have the same psi. Calls
reset_stats()
.- Parameters
model (
MPOModel
) – The model representing the Hamiltonian for which we want to find the ground state. IfNone
, keep the model used before.
Options
Deprecated since version 0.6.0: Options LP, LP_age, RP and RP_age are now collected in a dictionary init_env_data with different keys init_LP, init_RP, age_LP, age_RP
-
option
Sweep
.
init_env_data
: dict¶ Dictionary as returned by
self.env.get_initialization_data()
fromget_initialization_data()
.
-
option
Sweep
.
orthogonal_to
: list ofMPSEnvironment
¶ List of other matrix product states to orthogonalize against. Works only for finite systems. This parameter can be used to find (a few) excited states as follows. First, run DMRG to find the ground state and then run DMRG again while orthogonalizing against the ground state, which yields the first excited state (in the same symmetry sector), and so on.
-
option
Sweep
.
start_env
: int¶ Number of sweeps to be performed without optimization to update the environment.
- Raises
ValueError – If the engine is re-initialized with a new model, which legs are incompatible with those of hte old model.
-
config