def test_logneg_subsys_pure_should_swap_subsys(self):
p = qu.rand_ket(2**(5 + 2))
dims = (2**5, 2**2)
sysa = 0
sysb = 1
# exact 1
ln0 = qu.logneg(p, dims, 0)
# exact 2
ln1 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1e30)
assert_allclose(ln0, ln1)
# approx
ln2 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1, tol=0.005)
assert ln1 != ln2
assert_allclose(ln1, ln2, rtol=0.2)
def test_logneg_subsys_pure(self):
p = qu.rand_ket(2**(3 + 4))
dims = (2**3, 2**4)
sysa = 0
sysb = 1
# exact 1
ln0 = qu.logneg(p, dims, 0)
# exact 2
ln1 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1e30)
assert_allclose(ln0, ln1)
# approx
ln2 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1, tol=5e-3)
assert ln1 != ln2
assert_allclose(ln1, ln2, rtol=1e-1)
def test_logneg_subsys(self):
p = qu.rand_ket(2**(2 + 3 + 1 + 2))
dims = (2**2, 2**3, 2**1, 2**2)
sysa = [0, 3]
sysb = 1
# exact 1
ln0 = qu.logneg(qu.ptr(p, dims, [0, 1, 3]), [4, 8, 4], [0, 2])
# exact 2
ln1 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1e30)
assert_allclose(ln0, ln1)
# approx
ln2 = qu.logneg_subsys(p, dims, sysa, sysb, approx_thresh=1)
assert ln1 != ln2
assert_allclose(ln1, ln2, rtol=5e-2)
def test_heisenberg(self, n, l, gap):
ham = MPO_ham_heis(n)
dmrg = DMRG2(ham)
dmrg.solve()
gl = gap // 2
gr = gap // 2 + gap % 2
m = n // 2
sysa = range(m - l - gl, m - gl)
sysb = range(m + gr, m + l + gr)
assert max(sysa) + gap + 1 == min(sysb)
ln = dmrg.state.logneg_subsys(sysa,
sysb,
approx_spectral_opts={'bsz': 16},
verbosity=2)
# exact
lne = logneg_subsys(groundstate(ham_heis(n, cyclic=False)), [2] * n,
sysa, sysb)
assert_allclose(lne, ln, rtol=0.1, atol=0.1)
def test_realistic_ent(self):
n = 12
sysa, sysb = range(3, 6), range(6, 8)
ham = MPO_ham_heis(n)
dmrg = DMRG2(ham, bond_dims=[2, 4])
dmrg.solve()
rho_ab_pt = PTPTLazyMPS(dmrg.state, sysa, sysb)
psi0 = dmrg.state.to_dense()
lne = logneg_subsys(psi0, [2] * n, sysa=sysa, sysb=sysb)
lnx = log2(
approx_spectral_function(rho_ab_pt, abs, tol=0.1, verbosity=2))
assert_allclose(lne, lnx, rtol=0.5, atol=0.1)
def test_realistic_ent(self):
n = 12
sysa, sysb = range(3, 6), range(6, 8)
sysab = (*sysa, *sysb)
ham = MPO_ham_heis(n)
dmrg = DMRG2(ham, bond_dims=[10])
dmrg.solve()
psi0 = dmrg.state.to_dense()
lne = logneg_subsys(psi0, [2] * n, sysa=sysa, sysb=sysb)
rho_ab = dmrg.state.ptr(sysab, rescale_sites=True)
rho_ab_pt = rho_ab.partial_transpose(range(3))
lnx = log2(
approx_spectral_function(rho_ab_pt, abs, tol=0.1, verbosity=2))
assert_allclose(lne, lnx, rtol=0.6, atol=0.1)