def grow_block_by_one_site(growing_block, ground_state_wf, system,
number_of_states_kept):
"""Grows one side of the system by one site.
Calculates the truncation matrix by calculating the reduced density
matrix for `ground_state_wf` by tracing out the degrees of freedom of
the shrinking side. Then updates the operators you need in the next
steps, effectively growing the size of the block by one site.
Parameters
----------
growing_block : a string.
The block which is growing. It must be 'left' or 'right'.
ground_state_wf : a Wavefunction.
The ground state wavefunction of your system.
system : a System object.
The system you want to do the calculation on. This function
assumes that you have set the Hamiltonian to something.
number_of_states_kept : an int.
The number of states you want to keep in each block after the
truncation. If the `number_of_states_kept` is smaller than the
dimension of the current Hilbert space block, all states are kept.
Returns
-------
entropy : a double.
The Von Neumann entropy for the cut that splits the chain into two
equal halves.
truncation_error : a double.
The truncation error, i.e. the sum of the discarded eigenvalues of
the reduced density matrix.
Raises
------
DMRGException
if `growing_side` is not 'left' or 'right'.
"""
if growing_block not in ('left', 'right'):
raise DMRGException('Growing side must be left or right.')
system.set_growing_side(growing_block)
rho = ground_state_wf.build_reduced_density_matrix(growing_block)
evals, evecs = diagonalize(rho)
truncated_evals, truncation_matrix = truncate(evals, evecs,
number_of_states_kept)
entropy = calculate_entropy(truncated_evals)
truncation_error = calculate_truncation_error(truncated_evals)
set_block_hamiltonian_to_AF_Heisenberg(system)
set_operators_to_update_to_AF_Heisenberg(system)
system.update_all_operators(truncation_matrix)
return entropy, truncation_error
def grow_block_by_one_site(growing_block, ground_state_wf, system,
number_of_states_kept):
"""Grows one side of the system by one site.
Calculates the truncation matrix by calculating the reduced density
matrix for `ground_state_wf` by tracing out the degrees of freedom of
the shrinking side. Then updates the operators you need in the next
steps, effectively growing the size of the block by one site.
Parameters
----------
growing_block : a string.
The block which is growing. It must be 'left' or 'right'.
ground_state_wf : a Wavefunction.
The ground state wavefunction of your system.
system : a System object.
The system you want to do the calculation on. This function
assumes that you have set the Hamiltonian to something.
number_of_states_kept : an int.
The number of states you want to keep in each block after the
truncation. If the `number_of_states_kept` is smaller than the
dimension of the current Hilbert space block, all states are kept.
Returns
-------
entropy : a double.
The Von Neumann entropy for the cut that splits the chain into two
equal halves.
truncation_error : a double.
The truncation error, i.e. the sum of the discarded eigenvalues of
the reduced density matrix.
Raises
------
DMRGException
if `growing_side` is not 'left' or 'right'.
"""
if growing_block not in ('left', 'right'):
raise DMRGException('Growing side must be left or right.')
system.set_growing_side(growing_block)
rho = ground_state_wf.build_reduced_density_matrix(growing_block)
evals, evecs = diagonalize(rho)
truncated_evals, truncation_matrix = truncate(evals, evecs,
number_of_states_kept)
entropy = calculate_entropy(truncated_evals)
truncation_error = calculate_truncation_error(truncated_evals)
set_block_hamiltonian_to_AF_Heisenberg(system)
set_operators_to_update_to_AF_Heisenberg(system)
system.update_all_operators(truncation_matrix)
return entropy, truncation_error
def trace_out_left_qbit_and_calculate_entropy(wf):
"""Calculates the entropy after tracing out the left qbit.
To calculate the entanglement entropy you need to first build the
reduced density matrix tracing out the degrees of freedom of one of
the two qbits (it does not matter which, we pick up left here.)
Parameters
----------
wf : a Wavefunction
The wavefunction you build up the reduced density matrix with.
Returns
-------
result : a double
The value of the von Neumann entanglement entropy after tracing
out the left qbit.
"""
reduced_DM_for_right_qbit = wf.build_reduced_density_matrix('left')
evals, evecs = diagonalize(reduced_DM_for_right_qbit)
result = calculate_entropy(evals)
return result
def trace_out_left_qbit_and_calculate_entropy(wf):
"""Calculates the entropy after tracing out the left qbit.
To calculate the entanglement entropy you need to first build the
reduced density matrix tracing out the degrees of freedom of one of
the two qbits (it does not matter which, we pick up left here.)
Parameters
----------
wf : a Wavefunction
The wavefunction you build up the reduced density matrix with.
Returns
-------
result : a double
The value of the von Neumann entanglement entropy after tracing
out the left qbit.
"""
reduced_DM_for_right_qbit = wf.build_reduced_density_matrix('left')
evals, evecs = diagonalize(reduced_DM_for_right_qbit)
result = calculate_entropy(evals)
return result