seemps.evolution.Trotter3rdOrder

class seemps.evolution.Trotter3rdOrder

Bases: Trotter

Class implementing a 3rd order Trotter algorithm.

This class implements a Trotter algorithm in TEBD form for a nearest-neighbor interaction Hamiltonain \(\sum_i h_{i,i+1}\). This third-order formula is a variation of the three-sweep algorithm

\[\prod_{j=1}^{N} \exp(-\frac{i}{4} h_{j,j+1} dt) \prod_{j=N}^{1} \exp(-\frac{i}{2} h_{j,j+1} dt) \prod_{j=1}^{N} \exp(-\frac{i}{4} h_{j,j+1} dt)\]

Parameters:

HNNHamiltonian

The Hamiltonian with nearest-neighbor interactions generating the unitary transformations.

dtfloat

Length of the time step.

strategyStrategy

Truncation strategy for the application of the unitaries.

apply(state: MPS) → CanonicalMPS

Apply a Trotter 2nd order unitary approximation onto an MPS state.

Parameters:

stateMPS

The state to be evolved.

Returns:

CanonicalMPS

A fresh new MPS wih the state evolved by one time step.

apply_inplace(state: MPS) → CanonicalMPS

Apply a Trotter 3rd order unitary approximation onto an MPS state.

Parameters:

stateMPS

The state to be evolved.

Returns:

CanonicalMPS

The same state object modified by the unitary, if it was a CanonicalMPS Otherwise a fresh new state evolved.