def eval_corrf_SS(self, state, env_c4v, dist):
# function generating properly rotated operators on every bi-partite site
def get_bilat_op(op):
rot_op = su2.get_rot_op(self.phys_dim,
dtype=self.dtype,
device=self.device)
op_0 = op
op_rot = torch.einsum('ki,kl,lj->ij', rot_op, op_0, rot_op)
def _gen_op(r):
return op_rot if r % 2 == 0 else op_0
return _gen_op
op_sx = 0.5 * (self.obs_ops["sp"] + self.obs_ops["sm"])
op_isy = -0.5 * (self.obs_ops["sp"] - self.obs_ops["sm"])
Sz0szR= corrf_c4v.corrf_1sO1sO(state, env_c4v, self.obs_ops["sz"], \
get_bilat_op(self.obs_ops["sz"]), dist)
Sx0sxR = corrf_c4v.corrf_1sO1sO(state, env_c4v, op_sx,
get_bilat_op(op_sx), dist)
nSy0SyR = corrf_c4v.corrf_1sO1sO(state, env_c4v, op_isy,
get_bilat_op(op_isy), dist)
res = dict({
"ss": Sz0szR + Sx0sxR - nSy0SyR,
"szsz": Sz0szR,
"sxsx": Sx0sxR,
"sysy": -nSy0SyR
})
return res
def eval_corrf_SS(self, state, env_c4v, dist, canonical=False):
Sop_zxy = torch.zeros((3, self.phys_dim, self.phys_dim),
dtype=self.dtype,
device=self.device)
Sop_zxy[0, :, :] = self.obs_ops["sz"]
Sop_zxy[1, :, :] = 0.5 * (self.obs_ops["sp"] + self.obs_ops["sm"])
Sop_zxy[2, :, :] = -0.5 * (self.obs_ops["sp"] - self.obs_ops["sm"])
# compute vector of spontaneous magnetization
if canonical:
s_vec_zpm = []
rdm1x1 = rdm_c4v.rdm1x1(state, env_c4v)
for label in ["sz", "sp", "sm"]:
op = self.obs_ops[label]
s_vec_zpm.append(torch.trace(rdm1x1 @ op))
# 0) transform into zxy basis and normalize
s_vec_zxy= torch.tensor([s_vec_zpm[0],0.5*(s_vec_zpm[1]+s_vec_zpm[2]),\
0.5*(s_vec_zpm[1]-s_vec_zpm[2])],dtype=self.dtype,device=self.device)
s_vec_zxy = s_vec_zxy / torch.norm(s_vec_zxy)
# 1) build rotation matrix
R= torch.tensor([[s_vec_zxy[0],-s_vec_zxy[1],0],[s_vec_zxy[1],s_vec_zxy[0],0],[0,0,1]],\
dtype=self.dtype,device=self.device).t()
# 2) rotate the vector of operators
Sop_zxy = torch.einsum('ab,bij->aij', R, Sop_zxy)
# function generating properly rotated operators on every bi-partite site
def get_bilat_op(op):
rot_op = su2.get_rot_op(self.phys_dim,
dtype=self.dtype,
device=self.device)
op_0 = op
op_rot = torch.einsum('ki,kl,lj->ij', rot_op, op_0, rot_op)
def _gen_op(r):
return op_rot if r % 2 == 0 else op_0
return _gen_op
Sz0szR= corrf_c4v.corrf_1sO1sO(state, env_c4v, Sop_zxy[0,:,:], \
get_bilat_op(Sop_zxy[0,:,:]), dist)
Sx0sxR = corrf_c4v.corrf_1sO1sO(state, env_c4v, Sop_zxy[1, :, :],
get_bilat_op(Sop_zxy[1, :, :]), dist)
nSy0SyR = corrf_c4v.corrf_1sO1sO(state, env_c4v, Sop_zxy[2, :, :],
get_bilat_op(Sop_zxy[2, :, :]), dist)
res = dict({
"ss": Sz0szR + Sx0sxR - nSy0SyR,
"szsz": Sz0szR,
"sxsx": Sx0sxR,
"sysy": -nSy0SyR
})
return res
def eval_corrf_SS(self, state, env_c4v, dist):
Sop_zxy = torch.zeros((3, self.phys_dim, self.phys_dim),
dtype=self.dtype,
device=self.device)
Sop_zxy[0, :, :] = self.obs_ops["sz"]
Sop_zxy[1, :, :] = 0.5 * (self.obs_ops["sp"] + self.obs_ops["sm"]
) # S^x
# dummy function, since no sublattice rotation is present
def get_op(op):
op_0 = op
def _gen_op(r):
return op_0
return _gen_op
Sz0szR = corrf_c4v.corrf_1sO1sO(state, env_c4v, Sop_zxy[0, :, :],
get_op(Sop_zxy[0, :, :]), dist)
Sx0sxR = corrf_c4v.corrf_1sO1sO(state, env_c4v, Sop_zxy[1, :, :],
get_op(Sop_zxy[1, :, :]), dist)
res = dict({"ss": Sz0szR + Sx0sxR, "szsz": Sz0szR, "sxsx": Sx0sxR})
return res