lattice

This module provides functions to define the 3D lattice

Functions

NNNcontact(v3NF, lattice, myL[, spin, isospin])

computes matrix elements for three-body onsite contact

Tkin(lattice, myL[, spin, isospin])

computes 1-body kinetic energy matrix elements.

contacts(vT1, vS1, lattice, myL[, spin, isospin])

computes matrix elements for 2-body onsite contacts

get_lattice(myL)

builds a 3D lattice

get_sp_basis(myL[, spin, isospin])

builds a 3D lattice for nucleons with spin isospin degrees of freedom

left(site, myL)

moves a site to the left in 1D, respecting periodic boundary conditions

makeState(x, y, z, tz, sz)

Takes position in x, y, and z on the lattice as well as the spin and isospin and returns a state

p_x(lattice, myL[, spin, isospin])

computes matrix elements for 1-body momentum operator p_x.

p_y(lattice, myL[, spin, isospin])

computes matrix elements for 1-body momentum operator p_y.

p_z(lattice, myL[, spin, isospin])

computes matrix elements for 1-body momentum operator p_z.

phys_unit(a_lat)

returns the energy unit from basic units

right(site, myL)

moves a site to the right in 1D, respecting periodic boundary conditions

site2index(site, myL)

given a site list [i,j,k] this function returns the index of that state in the list returned by get_lattice

state2index(state, myL[, spin, isospin])

given a state list [i,j,k,tz,sz] this function returns the index of that state in the list returned by get_sp_basis

states2PHSpace(holeList, myL)

Takes a list of hole states and returns the hole and particle spaces
lattice.phys_unit(a_lat)

returns the energy unit from basic units

Parameters:

a_lat (float) – lattice spacing in fm

Returns:

factor to scale the lattice units to energy units

Return type:

float

lattice.get_sp_basis(myL, spin=2, isospin=2)

builds a 3D lattice for nucleons with spin isospin degrees of freedom

Parameters:

  • myL (int) – number of lattice sites in each direction

  • spin (int) – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

List of integer list [i,j,k,tz,sz] where lattice sites are labelled by i, j, k (from 0 to myL-1) in direction 1, 2, 3; tz=0, 1 and sz=0,1 correspond to isospin tz-1/2 and spin sz-1/2, respectively

Return type:

list[(int, int, int, int, int)]

lattice.state2index(state, myL, spin=2, isospin=2)

given a state list [i,j,k,tz,sz] this function returns the index of that state in the list returned by get_sp_basis

Parameters:

  • state (list[(int, int, int, int, int)]) – the list [i,j,k,tz,sz]

  • myL (int) – number of lattice sites in each direction

  • spin (int) – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

index as an integer

Return type:

int

lattice.get_lattice(myL)

builds a 3D lattice

Parameters:

myL (int) – number of lattice sites in each direction

Returns:

List of integer lists [i,j,k] of lattice sites are labelled by i, j, k (from 0 to myL-1) in direction 1, 2, 3

Return type:

list[(int, int, int)]

lattice.site2index(site, myL)

given a site list [i,j,k] this function returns the index of that state in the list returned by get_lattice

Parameters:

  • state (list[(int, int, int)]) – the list [i,j,k]

  • myL (int) – number of lattice sites in each direction

Returns:

index as an integer

Return type:

int

lattice.right(site, myL)

moves a site to the right in 1D, respecting periodic boundary conditions

Parameters:

  • site (int) – integer location of the site

  • myL (int) – number of lattice sites in each direction

Returns:

index of site one to the right of site with index site

Return type:

int

lattice.left(site, myL)

moves a site to the left in 1D, respecting periodic boundary conditions

Parameters:

  • site (int) – integer location of the site

  • myL (int) – number of lattice sites in each direction

Returns:

index of site one to the left of site with index site

Return type:

int

lattice.Tkin(lattice, myL, spin=2, isospin=2)

computes 1-body kinetic energy matrix elements. Really: the negative dimensionless laplacian

Parameters:

  • lattice (list[(int, int, int)]) – list of lattice sites returned by get_lattice

  • myL (int) – number of lattice sites in each direction

  • spin (int) – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

list of tuples [i, j, value] where i and j are indices in the single-particle basis, and value is the value of the matrix element Tij

Return type:

list[(int, int, float)]

lattice.contacts(vT1, vS1, lattice, myL, spin=2, isospin=2)

computes matrix elements for 2-body onsite contacts

Parameters:

  • vT1 (float) – strength of T=1 coupling

  • vS1 (float) – strength of S=1 coupling

  • lattice (list[(int, int, int)]) – list of lattice sites returned by get_lattice

  • myL (int) – number of lattice sites in each direction

  • spin (int) – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

list of lists [i, j, k, l, value] where i, j and k, l are indices of two particles in the single-particle basis, and value is the value of the matrix element <ij||kl>. All elements have i<j and k<l

Return type:

list[(int, int, int, int, float)]

lattice.NNNcontact(v3NF, lattice, myL, spin=2, isospin=2)

computes matrix elements for three-body onsite contact

Parameters:

  • v3NF (float) – strength of the 3 nucleon force

  • lattice (list[(int, int, int)]) – list of lattice sites returned by get_lattice

  • myL (int) – number of lattice sites in each direction

  • spin – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

list of tuples [i1, i2, i3, j1, j2, j3, value] where i1, i2, i3 and j1, j2, j3 are indices of three particles in the single-particle basis, and value is one (unit strength) for the matrix element <i1 i2 i3||j1 j2 j3>. All elements have i1<i2<i3 and j1<j2<j3

Return type:

list[(int, int, int, int, int, int, float)]

lattice.p_x(lattice, myL, spin=2, isospin=2)

computes matrix elements for 1-body momentum operator p_x. Really: -i times d_x

Parameters:

  • lattice (list[(int, int, int)]) – list of lattice sites returned by get_lattice

  • myL (int) – number of lattice sites in each direction

  • spin – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

list of tuples [i, j, value] where i and j are indices in the single-particle basis, and value is the value of the matrix element Tij

Return type:

list[(int, int, float)]

lattice.p_y(lattice, myL, spin=2, isospin=2)

computes matrix elements for 1-body momentum operator p_y. Really: -i times d_y

Parameters:

  • lattice (list[(int, int, int)]) – list of lattice sites returned by get_lattice

  • myL (int) – number of lattice sites in each direction

  • spin – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

list of tuples [i, j, value] where i and j are indices in the single-particle basis, and value is the value of the matrix element Tij

Return type:

list[(int, int, float)]

lattice.p_z(lattice, myL, spin=2, isospin=2)

computes matrix elements for 1-body momentum operator p_z. Really: -i times d_z

Parameters:

  • lattice (list[(int, int, int)]) – list of lattice sites returned by get_lattice

  • myL (int) – number of lattice sites in each direction

  • spin – Optional; number of spin degrees of freedom

  • isospin (int) – Optional; number of isospin degrees of freedom

Returns:

list of tuples [i, j, value] where i and j are indices in the single-particle basis, and value is the value of the matrix element Tij

Return type:

list[(int, int, float)]

lattice.states2PHSpace(holeList, myL)

Takes a list of hole states and returns the hole and particle spaces

Parameters:

  • holeList (list[(int, int, int, int, int)]) – list of holes and their sites as [i, j, k, tz, sz]

  • myL (int) – number of lattice sites in each direction

Returns:

hole and particle space

Return type:

tuple(int), tuple(int)

lattice.makeState(x, y, z, tz, sz)

Takes position in x, y, and z on the lattice as well as the spin and isospin and returns a state

Parameters:

  • x (int) – x position in lattice

  • y (int) – y position in lattice

  • z (int) – z position in lattice

  • tz (0.5 | -0.5) – isospin

  • sz (0.5 | -0.5) – spin

Returns:

a particle state on the lattice as a list

Return type:

list[(int, int, int, int, int)]