EngineFracture¶
full name: tenpy.algorithms.dmrg.EngineFracture
parent module:
tenpy.algorithms.dmrg
type: class
Inheritance Diagram
Methods

Initialize self. 

Diagonalize the effective Hamiltonian represented by self. 

Perform N_sweeps sweeps without optimization to update the environment. 
Define the schedule of the sweep. 


(Re)initialize the environment. 

Get (truncated) B from the new theta (as returned by diag). 
Set self.mixer to the class specified by engine_params[‘mixer’]. 

Cleanup the effects of a mixer. 


Plot 

Plot 

Perform postupdate actions. 

Transform theta into matrix for svd. 
Prepare self to represent the effective Hamiltonian on sites 

Reset the statistics, useful if you want to start a new sweep run. 

Run the DMRG simulation to find the ground state. 


Update the MPS with the 

One ‘sweep’ of a sweeper algorithm. 
Update left part of the environment. 

Update right part of the environment. 


Perform bondupdate on the sites 

class
tenpy.algorithms.dmrg.
EngineFracture
(psi, model, DMRG_params)[source]¶ Bases:
tenpy.algorithms.dmrg.TwoSiteDMRGEngine
Engine which keeps the legs separate.
Due to a different contraction order in
matvec()
, this engine might be faster thanEngineCombine
, at least for large physical dimensions and if the MPO is sparse. Onematvec()
is \(O(2 \chi^3 d^2 W + 2 \chi^2 d^3 W^2 )\).
diag
(theta_guess)[source]¶ Diagonalize the effective Hamiltonian represented by self.
The method used depends on the DMRG parameter diag_method.
diag_method
Function, comment
‘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_guesstheta_diag>)

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. Raises
ValueError – If the engine is reinitialized with a new model, which legs are incompatible with those of hte old model.

mixed_svd
(theta)[source]¶ Get (truncated) B from the new theta (as returned by diag).
The goal is to split theta and truncate it:
  theta  ==>  U  S  VH      
Without a mixer, this is done by a simple svd and truncation of Schmidt values.
With a mixer, the state is perturbed before the SVD. The details of the perturbation are defined by the
Mixer
class.Note that the returned S is a general (not diagonal) matrix, with labels
'vL', 'vR'
. Parameters
theta (
Array
) – The optimized wave function, prepared for svd. Returns
U (
Array
) – Leftcanonical part of theta. Labels'(vL.p0)', 'vR'
.S (1D ndarray  2D
Array
) – Without mixer just the singluar values of the array; with mixer it might be a general matrix with labels'vL', 'vR'
; see comment above.VH (
Array
) – Rightcanonical part of theta. Labels'vL', '(p1.vR)'
.err (
TruncationError
) – The truncation error introduced.

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.

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 xaxis and yaxis of the plots.y_exact (float) – Exact value for the quantity on the yaxis for comparison. If given, plot
abs((yy_exact)/y_exact)
on a logscale yaxis.**kwargs – Further keyword arguments given to
axes.plot(...)
.

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 xaxis 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 yaxisof the plots. For ‘E’, use the energy (per site for infinite systems).y_exact (float) – Exact value for the quantity on the yaxis for comparison. If given, plot
abs((yy_exact)/y_exact)
on a logscale yaxis.**kwargs – Further keyword arguments given to
axes.plot(...)
.

post_update_local
(update_data, meas_E_trunc=False)[source]¶ Perform postupdate actions.
Compute truncation energy, remove LP/RP that are no longer needed and collect statistics.

prepare_update
()[source]¶ Prepare self to represent the effective Hamiltonian on sites
(i0, i0+1)
. Returns
theta – Current best guess for the ground state, which is to be optimized. Labels
'vL', 'p0', 'vR', 'p1'
. Return 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
.

set_B
(U, S, VH)[source]¶ Update the MPS with the
U, S, VH
returned by self.mixed_svd. Parameters
VH (U,) – Left and Rightcanonical matrices as returned by the SVD.
S (1D array  2D
Array
) – The middle part returned by the SVD,theta = U S VH
. Without a mixer just the singular values, with enabled mixer a 2D array.

sweep
(optimize=True, meas_E_trunc=False)[source]¶ One ‘sweep’ of a sweeper algorithm.
Iteratate over the bond which is optimized, to the right and then back to the left to the starting point. If optimize=False, don’t actually diagonalize the effective hamiltonian, but only update the environment.
 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.

update_LP
(U)[source]¶ Update left part of the environment.
We always update the environment at site i0 + 1: this environment then contains the site where we just performed a local update (when sweeping right).
 Parameters
U (
Array
) – The U as returned by the SVD, with combined legs, labels'vL.p0', 'vR'
.

update_RP
(VH)[source]¶ Update right part of the environment.
We always update the environment at site i0: this environment then contains the site where we just performed a local update (when sweeping left).
 Parameters
VH (
Array
) – The VH as returned by SVD, with combined legs, labels'vL', '(vR.p1)'
.

update_local
(theta, optimize=True, meas_E_trunc=False)[source]¶ Perform bondupdate on the sites
(i0, i0+1)
. Parameters
 Returns
update_data – Data computed during the local update, as described in the following:
 E0float
Total energy, obtained before truncation (if
optimize=True
), or after truncation (ifoptimize=False
) (but neverNone
). Nint
Dimension of the Krylov space used for optimization in the lanczos algorithm. 0 if
optimize=False
. ageint
Current size of the DMRG simulation: number of physical sites involved into the contraction.
 U, VH:
Array
U and VH returned by
mixed_svd()
. ov_change: float
Change in the wave function
1.  abs(<theta_guesstheta>)
induced bydiag()
, not including the truncation!
 Return type
