Exact diagonalization for lattice gauge theories using the QuSpin package for python.
Create an object of the Z2 class, which represent a Z2 lattice pure
gauge theory (no matter) on 3x3 lattice with periodic boundary condition:
from qulgt import Z2
z2_lgt = Z2(size=(3, 3), pbc=(True, True))
or you can create it on a 10x2 ladder with periodic condition only along the x
direction:
z2_ladder = Z2(size=(3,3), pbc=(True, False))
The Z2 class accepts two keyword arguments: size and pbc. The first one has
to be a tuple of two integers, the second a tuple of two boolean.
The size keyword arg specifies the dimension of the lattice (in terms of
sites), while pbc whether or not to implements periodic boundary conditions.
The first value of the tuples always refers to the x direction, while the
second to the y direction.
The class accepts also a third keyword argument sector, which can restrict
the Hilbert space to a particular sector between (0, 0), (1, 0), (0, 1) and
(1, 1). The sectors are distinguished by the parity of the number of
non-contractible electric loops along the x or y direction respectively.
The 0 sign refers to an even number of loops, while 1 to an odd number.
For example:
z2_lgt = Z2(size=(3, 3), pbc=(True, True), sector=(0, 0))
On the other hand, if we want to explicitly work with the whole gauge invariant Hilbert space:
z2_lgt = Z2(size=(3, 3), pbc=(True, True), sector=None)