Lattice geometry#

We generate a square lattice geometries and verify the expected output of its methods. It checks the dimensions, sites, bonds, and nearest neighbor sites of the lattice. The function is tested on an infinite checkerboard lattice and a finite square lattice with open boundary conditions.

import pytest
import yastn
import yastn.tn.fpeps as fpeps
from yastn.tn.fpeps import Bond, Site

def test_CheckerboardLattice(net=None):
    """ Test checkerboard lattice. """
    if net is None:
        net = fpeps.CheckerboardLattice()

    assert net.dims == (2, 2)  # size of unit cell
    assert net.sites() == (Site(0, 0), Site(0, 1))  # two unique sites
    assert net.sites(reverse=True) == (Site(0, 1), Site(0, 0))
    assert net._periodic == 'ii'  # lattice is infinite in both directions.

    # unique horizontal bonds
    assert net.bonds(dirn='h') == (Bond((0, 0), (0, 1)), Bond((0, 1), (0, 2)))
    # unique vertical bonds
    assert net.bonds(dirn='v') == (Bond((0, 0), (1, 0)), Bond((0, 1), (1, 1)))
    # all unique bonds; also in reversed order
    assert net.bonds(reverse=True)[::1] == net.bonds()[::-1]

    # map from site to unique index
    # it is used in Peps.__getitem__(site);  EncCTM.__getitem__(site), ...
    assert all(net.site2index(site) == 0
               for site in [(0, 0), (1, 1), (-3, 3), (1, -1), (2, 0)])
    assert all(net.site2index(site) == 1
               for site in [(1, 0), (0, 1), (2, 5), (1, 2), (-1, 0)])

    # nearest-neighbor site to: right, left, top, bottom
    assert net.nn_site(Site(1, 1), d='r') == (1, 2)
    assert net.nn_site(Site(1, 0), d='l') == (1, -1)
    assert net.nn_site(Site(0, 0), d='t') == (-1, 0)
    assert net.nn_site(Site(1, 0), d='b') == (2, 0)

    # whether a nearest-neighbor bond is horizontal or vertical and
    # whether it is ordered as (left, right) or (top, bottom) lattice sites.
    assert net.nn_bond_type(Bond((0, 0), (0, 1))) == ('h', True)  # 'lr'
    assert net.nn_bond_type(Bond((0, 3), (0, 2))) == ('h', False) # 'rl'
    assert net.nn_bond_type(Bond((1, 3), (0, 3))) == ('v', False) # 'bt'
    assert net.nn_bond_type(Bond((1, 0), (2, 0))) == ('v', True)  # 'tb'
    with pytest.raises(yastn.YastnError):
        net.nn_bond_type(Bond((1, 0), (3, 0)))
        # Bond((1, 0),(3, 0)) is not a nearest-neighbor bond.

    # order of bonds in net.bond()
    assert all(net.nn_bond_type(bond) == ('h', True)
               for bond in net.bonds(dirn='h'))
    assert all(net.nn_bond_type(bond) == ('v', True)
               for bond in net.bonds(dirn='v'))

    # pairs of sites consistent with the assumed fermionic order.
    assert net.f_ordered((2, 0), (4, 0))
    assert net.f_ordered((4, 0), (0, 4))
    assert all(net.f_ordered(s0, s1)
               for s0, s1 in zip(net.sites(), net.sites()[1:]))
    assert all(net.f_ordered(*bond) for bond in net.bonds())

def test_SquareLattice_obc():
    """ Test SquareLattice with open boundary conditions. """
    net = fpeps.SquareLattice(dims=(3, 2), boundary='obc')

    assert net.dims == (3, 2)  # size of unit cell
    # sites in the lattice
    assert net.sites() == ((0, 0), (1, 0), (2, 0), (0, 1), (1, 1), (2, 1))
    # horizontal bonds
    assert net.bonds(dirn='h') == (Bond((0, 0), (0, 1)),
                                   Bond((1, 0), (1, 1)),
                                   Bond((2, 0), (2, 1)))
    # vertical bonds
    assert net.bonds(dirn='v') == (Bond((0, 0), (1, 0)),
                                   Bond((1, 0), (2, 0)),
                                   Bond((0, 1), (1, 1)),
                                   Bond((1, 1), (2, 1)))
    #
    # Lattice has open boundary conditions in both directions.
    assert net._periodic == 'oo'
    #
    # no nearest-neighbor sites from some edges in some directions
    assert net.nn_site((0, 1), d='r') is None
    assert net.nn_site((0, 1), d='t') is None
    assert net.nn_site((2, 0), d='l') is None
    assert net.nn_site((2, 0), d='b') is None
    assert net.nn_site(None, d='l') is None
    #
    # nn_site can shift by more then 1 site.
    assert net.nn_site((0, 1), d=(2, -1)) == Site(2, 0)
    #
    # trivial map from site to unique index
    assert net.site2index((1, 0)) == (1, 0)
    assert net.site2index(None) == None

    # whether a nearest-neighbor bond is horizontal or vertical and
    # whether it is ordered as (left, right) or (top, bottom) lattice sites.
    assert net.nn_bond_type(Bond((0, 0), (0, 1))) == ('h', True)  # 'lr'
    assert net.nn_bond_type(Bond((0, 1), (0, 0))) == ('h', False) # 'rl'
    assert net.nn_bond_type(Bond((2, 1), (1, 1))) == ('v', False) # 'bt'
    assert net.nn_bond_type(Bond((1, 0), (2, 0))) == ('v', True)  # 'tb'
    with pytest.raises(yastn.YastnError):
        net.nn_bond_type(Bond((0, 0), (2, 0)))
        # Bond((0, 0), (2, 0)) is not a nearest-neighbor bond.

    # order of bonds in net.bond()
    assert all(net.nn_bond_type(bond) == ('h', True)
               for bond in net.bonds(dirn='h'))
    assert all(net.nn_bond_type(bond) == ('v', True)
               for bond in net.bonds(dirn='v'))

    # pairs of sites consistent with the assumed fermionic order.
    assert net.f_ordered((0, 0), (1, 0))
    assert net.f_ordered((0, 0), (0, 1))
    assert net.f_ordered((1, 0), (0, 1))
    assert all(net.f_ordered(s0, s1)
               for s0, s1 in zip(net.sites(), net.sites()[1:]))
    assert all(net.f_ordered(*bond) for bond in net.bonds())

test_CheckerboardLattice()
test_SquareLattice_obc()

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