Engine¶
full name: tenpy.algorithms.tebd.Engine
parent module:
tenpy.algorithms.tebd
type: class
Inheritance Diagram
Methods
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Calculate |
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Return necessary data to resume a |
Resume a run that was interrupted. |
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Run TEBD real time evolution by N_steps`*`dt. |
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TEBD algorithm in imaginary time to find the ground state. |
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Returns list of necessary steps for the suzuki trotter decomposition. |
Return time steps of U for the Suzuki Trotter decomposition of desired order. |
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Evolve by |
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Updates the B matrices on a given bond. |
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Update a bond with a (possibly non-unitary) U_bond. |
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Perform an update suitable for imaginary time evolution. |
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Updates either even or odd bonds in unit cell. |
Class Attributes and Properties
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whether the algorithm supports time-dependent H |
truncation error introduced on each non-trivial bond. |
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- class tenpy.algorithms.tebd.Engine(psi, model, options)[source]¶
Bases:
tenpy.algorithms.tebd.TEBDEngine
Deprecated old name of
TEBDEngine
.- calc_U(order, delta_t, type_evo='real', E_offset=None)[source]¶
Calculate
self.U_bond
fromself.bond_eig_{vals,vecs}
.This function calculates
U_bond = exp(-i dt (H_bond-E_offset_bond))
fortype_evo='real'
, orU_bond = exp(- dt H_bond)
fortype_evo='imag'
.
For first order (in delta_t), we need just one
dt=delta_t
. Higher order requires smaller dt steps, as given bysuzuki_trotter_time_steps()
.- Parameters
order (int) – Trotter order calculated U_bond. See update for more information.
delta_t (float) – Size of the time-step used in calculating U_bond
type_evo (
'imag' | 'real'
) – Determines whether we perform real or imaginary time-evolution.E_offset (None | list of float) – Possible offset added to H_bond for real-time evolution.
- get_resume_data(sequential_simulations=False)[source]¶
Return necessary data to resume a
run()
interrupted at a checkpoint.At a
checkpoint
, you can savepsi
,model
andoptions
along with the data returned by this function. When the simulation aborts, you can resume it using this saved data with:eng = AlgorithmClass(psi, model, options, resume_data=resume_data) eng.resume_run()
An algorithm which doesn’t support this should override resume_run to raise an Error.
- Parameters
sequential_simulations (bool) – If True, return only the data for re-initializing a sequential simulation run, where we “adiabatically” follow the evolution of a ground state (for variational algorithms), or do series of quenches (for time evolution algorithms); see
run_seq_simulations()
.- Returns
resume_data – Dictionary with necessary data (apart from copies of psi, model, options) that allows to continue the simulation from where we are now. It might contain an explicit copy of psi.
- Return type
- resume_run()[source]¶
Resume a run that was interrupted.
In case we saved an intermediate result at a
checkpoint
, this function allows to resume therun()
of the algorithm (after re-initialization with the resume_data). Since most algorithms just have a while loop with break conditions, the default behaviour implemented here is to just callrun()
.
- run_GS()[source]¶
TEBD algorithm in imaginary time to find the ground state.
Note
It is almost always more efficient (and hence advisable) to use DMRG. This algorithms can nonetheless be used quite well as a benchmark and for comparison.
- option TEBDEngine.delta_tau_list: list¶
A list of floats: the timesteps to be used. Choosing a large timestep delta_tau introduces large (Trotter) errors, but a too small time step requires a lot of steps to reach
exp(-tau H) --> |psi0><psi0|
. Therefore, we start with fairly large time steps for a quick time evolution until convergence, and the gradually decrease the time step.
- option TEBDEngine.order: int¶
Order of the Suzuki-Trotter decomposition.
- option TEBDEngine.N_steps: int¶
Number of steps before measurement can be performed
- static suzuki_trotter_decomposition(order, N_steps)[source]¶
Returns list of necessary steps for the suzuki trotter decomposition.
We split the Hamiltonian as \(H = H_{even} + H_{odd} = H[0] + H[1]\). The Suzuki-Trotter decomposition is an approximation \(\exp(t H) \approx prod_{(j, k) \in ST} \exp(d[j] t H[k]) + O(t^{order+1 })\).
- Parameters
order (
1, 2, 4, '4_opt'
) – The desired order of the Suzuki-Trotter decomposition. Order1
approximation is simply \(e^A a^B\). Order2
is the “leapfrog” e^{A/2} e^B e^{A/2}. Order4
is the fourth-order from [suzuki1991] (also referenced in [schollwoeck2011]), and'4_opt'
gives the optmized version of Equ. (30a) in [barthel2020].- Returns
ST_decomposition – Indices
j, k
of the time-stepsd = suzuki_trotter_time_step(order)
and the decomposition of H. They are chosen such that a subsequent application ofexp(d[j] t H[k])
to a given state|psi>
yields(exp(N_steps t H[k]) + O(N_steps t^{order+1}))|psi>
.- Return type
- static suzuki_trotter_time_steps(order)[source]¶
Return time steps of U for the Suzuki Trotter decomposition of desired order.
See
suzuki_trotter_decomposition()
for details.- Parameters
order (int) – The desired order of the Suzuki-Trotter decomposition.
- Returns
time_steps – We need
U = exp(-i H_{even/odd} delta_t * dt)
for the dt returned in this list.- Return type
list of float
- property trunc_err_bonds¶
truncation error introduced on each non-trivial bond.
- update(N_steps)[source]¶
Evolve by
N_steps * U_param['dt']
.- Parameters
N_steps (int) – The number of steps for which the whole lattice should be updated.
- Returns
trunc_err – The error of the represented state which is introduced due to the truncation during this sequence of update steps.
- Return type
- update_bond(i, U_bond)[source]¶
Updates the B matrices on a given bond.
Function that updates the B matrices, the bond matrix s between and the bond dimension chi for bond i. The correponding tensor networks look like this:
| --S--B1--B2-- --B1--B2-- | | | | | | theta: U_bond C: U_bond | | | | |
- Parameters
- Returns
trunc_err – The error of the represented state which is introduced by the truncation during this update step.
- Return type
- update_bond_imag(i, U_bond)[source]¶
Update a bond with a (possibly non-unitary) U_bond.
Similar as
update_bond()
; but after the SVD just keep the A, S, B canonical form. In that way, one can sweep left or right without using old singular values, thus preserving the canonical form during imaginary time evolution.- Parameters
- Returns
trunc_err – The error of the represented state which is introduced by the truncation during this update step.
- Return type
- update_imag(N_steps)[source]¶
Perform an update suitable for imaginary time evolution.
Instead of the even/odd brick structure used for ordinary TEBD, we ‘sweep’ from left to right and right to left, similar as DMRG. Thanks to that, we are actually able to preserve the canonical form.
- Parameters
N_steps (int) – The number of steps for which the whole lattice should be updated.
- Returns
trunc_err – The error of the represented state which is introduced due to the truncation during this sequence of update steps.
- Return type
- update_step(U_idx_dt, odd)[source]¶
Updates either even or odd bonds in unit cell.
Depending on the choice of p, this function updates all even (
E
, odd=False,0) or odd (O
) (odd=True,1) bonds:| - B0 - B1 - B2 - B3 - B4 - B5 - B6 - | | | | | | | | | | |----| |----| |----| | | | E | | E | | E | | | |----| |----| |----| | |----| |----| |----| | | | O | | O | | O | | | |----| |----| |----| |
Note that finite boundary conditions are taken care of by having
Us[0] = None
.- Parameters
U_idx_dt (int) – Time step index in
self._U
, evolve withUs[i] = self.U[U_idx_dt][i]
at bond(i-1,i)
.odd (bool/int) – Indication of whether to update even (
odd=False,0
) or even (odd=True,1
) sites
- Returns
trunc_err – The error of the represented state which is introduced due to the truncation during this sequence of update steps.
- Return type