# Hamiltonian¶

class Hamiltonian(N)[source]

Bases: object

Contains methods for initializing, creating and manipulating Hamiltonian matrices.

Parameters: N (int) – number of nodes to initialize the Hamiltonian object with. : creates an unallocated PETSc matrix on communicator petsc4py.PETSc.COMM_WORLD. This is accessed via the attribute Hamiltonian.mat. petsc4py.PETSc.Mat : an associated EigSolver object is also created at Hamiltonian.EigSolver. EigSolver

## Method Summary¶

 Hamiltonian.Emax(**kwargs) Returns the maximum Eigenvalue of the matrix. Hamiltonian.Emin(**kwargs) Returns the minimum Eigenvalue of the matrix. Hamiltonian.createLine([d, amp]) Create a 1 particle infinite line Hamiltonian. Hamiltonian.createLine2P([d, amp, interaction]) Create a 2 particle infinite line Hamiltonian. Hamiltonian.createLine3P([d, amp, interaction]) Create a 3 particle infinite line Hamiltonian. Hamiltonian.destroy() Destroys all associated PETSc matrices. Hamiltonian.importAdj(filename, filetype[, ...]) Create a Hamiltonian from an imported adjacency matrix. Hamiltonian.importAdjToH(filename, filetype) Create a Hamiltonian from an imported adjacency matrix. Hamiltonian.reinitialize() Destroy and reinitialize the PETSc matrix Hamiltonian.mat.

## Method Details¶

Hamiltonian.Emax(**kwargs)[source]

Returns the maximum Eigenvalue of the matrix.

Example

>>> Emax = Hamiltonian.Emax()

Hamiltonian.Emin(**kwargs)[source]

Returns the minimum Eigenvalue of the matrix.

Example

>>> Emin = Hamiltonian.Emin()

Hamiltonian.createLine(d=, amp=[0.0])[source]

Create a 1 particle infinite line Hamiltonian.

Parameters: d (array of ints) – an array containing integers indicating the nodes where diagonal defects are to be placed (e.g. d=[0,1,4]). amp (array of floats) – an array containing floats indicating the diagonal defect amplitudes corresponding to each element in d (e.g. amp=[0.5,-1,4.2]). interaction (float) – the amplitude of interaction between the walkers when located on the same vertex. : Hamiltonian.mat, the Hamiltonian matrix. petsc4py.PETSc.Mat()

Important

• The length of amp and d must be identical.

Fortran interface

This function calls the Fortran function hamiltonian_p1_line().

Hamiltonian.createLine2P(d=, amp=[0.0], interaction=0.0)[source]

Create a 2 particle infinite line Hamiltonian.

Parameters: d (array of ints) – an array containing integers indicating the nodes where diagonal defects are to be placed (e.g. d=[0,1,4]). amp (array of floats) – an array containing floats indicating the diagonal defect amplitudes corresponding to each element in d (e.g. amp=[0.5,-1,4.2]). interaction (float) – the amplitude of interaction between the walkers when located on the same vertex. : Hamiltonian.mat, the Hamiltonian matrix. petsc4py.PETSc.Mat()

Important

• The length of amp and d must be identical.

Fortran interface

This function calls the Fortran function hamiltonian_p2_line().

Hamiltonian.createLine3P(d=, amp=[0.0], interaction=0.0)[source]

Create a 3 particle infinite line Hamiltonian.

Parameters: d (array of ints) – an array containing integers indicating the nodes where diagonal defects are to be placed (e.g. d=[0,1,4]). amp (array of floats) – an array containing floats indicating the diagonal defect amplitudes corresponding to each element in d (e.g. amp=[0.5,-1,4.2]). interaction (float) – the amplitude of interaction between the walkers when located on the same vertex. : Hamiltonian.mat, the Hamiltonian matrix. petsc4py.PETSc.Mat()

Important

• The length of amp and d must be identical.

Fortran interface

This function calls the Fortran function hamiltonian_p3_line().

Hamiltonian.destroy()[source]

Destroys all associated PETSc matrices.

Hamiltonian.importAdj(filename, filetype, d=, amp=[0.0], layout='spring', delimiter=None)[source]

Create a Hamiltonian from an imported adjacency matrix.

Parameters: filename (str) – path to the file containing the adjacency matrix of the graph filetype (str) – the filetype of the imported adjacency matrix. 'txt' - an $$N\times N$$ dense 2D array in text format. 'bin' - an $$N\times N$$ PETSc binary matrix. d (array of ints) – an array containing integers indicating the nodes where diagonal defects are to be placed (e.g. d=[0,1,4]). amp (array of floats) – an array containing floats indicating the diagonal defect amplitudes corresponding to each element in d (e.g. amp=[0.5,-1,4.2]). layout (str) – the format to store the position of the nodes. spring (default) - spring layout. circle - nodes are arranged in a circle. spectral - nodes are laid out according to the spectrum of the graph. random - nodes are arranged in a random pattern. delimiter (str) – this is passed to numpy.genfromtxt in the case of strange delimiters in an imported txt file. :this allocates and builds a Hamiltonian matrix at Hamiltonian.mat. petsc4py.PETSc.Mat() : the original adjacency matrix is also stored as a PETSc matrix at Hamiltonian.Adj. petsc4py.PETSc.Mat()

Important

• The number of nodes in the imported adjacency matrix must match the number of nodes the Hamiltonian object is initialized with.
• The length of amp and d must be identical.

Note

• This function calls Python functions located at pyCTQW.MPI.io, and is somewhat slower than importAdjToH(), but with the advantage of a more flexible text file importer.
• For the ability to generate 2 or 3 particle Hamiltonians with or without interactions, please see importAdjToH().
Hamiltonian.importAdjToH(filename, filetype, d=[0.0], amp=[0.0], p='1', layout='spring', delimiter=None, interaction=0.0, bosonic=False)[source]

Create a Hamiltonian from an imported adjacency matrix.

Args:

filename (str): path to the file containing the adjacency matrix of the graph

filetype (str): the filetype of the imported adjacency matrix.

• 'txt' - an $$N\times N$$ dense 2D array in text format.
• 'bin' - an $$N\times N$$ PETSc binary matrix.
d (array of ints): an array containing integers indicating the nodes
where diagonal defects are to be placed (e.g. d=[0,1,4]).
amp (array of floats): an array containing floats indicating the diagonal defect
amplitudes corresponding to each element in d (e.g. amp=[0.5,-1,4.2]).

p (str) : ('1'|‘2’|‘3’) - specify whether to create a 1, 2 or 3 particle Hamiltonian.

layout (str): the format to store the position of the nodes.

• spring (default) - spring layout.
• circle - nodes are arranged in a circle.
• spectral - nodes are laid out according to the spectrum of the graph.
• random - nodes are arranged in a random pattern.
delimiter (str): this is passed to numpy.genfromtxt
in the case of strange delimiters in an imported txt file.

interaction (float): the amplitude of interaction between the walkers when located on the same vertex.

bosonic (bool): if true, a Bosonic Hamiltonian is generated.

Returns:
: * Hamiltonian.mat (petsc4py.PETSc.Mat) - the Hamiltonian matrix.
• Hamiltonian.Adj (petsc4py.PETSc.Mat) - the adjacency matrix stored as a PETSc matrix.
• Hamiltonian.nodePos (array) - the $$(x,y)$$ coordinates of the graph vertices.
• Hamiltonian.lineX (array) - the $$x$$ coordinates of the edges connecting graph vertices.
• Hamiltonian.lineY (array) - the $$y$$ coordinates of the edges connecting graph vertices.

Important

• The number of nodes in the imported adjacency matrix must match the number of nodes the Hamiltonian object is initialized with.
• The length of amp and d must be identical.

Fortran interface

This function calls the Fortran function importadjtoh() and is faster than importAdjToH(), but with a ‘pickier’ text file importer.

Hamiltonian.reinitialize()[source]

Destroy and reinitialize the PETSc matrix Hamiltonian.mat.