def test_dtypes(self, dtype):
H = MPO_ham_heis(8).astype(dtype)
dmrg = DMRG2(H)
dmrg.opts['local_eig_backend'] = 'scipy'
dmrg.solve(max_sweeps=3)
res_dtype, = {t.dtype for t in dmrg.state}
assert res_dtype == dtype
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_cyclic_solve_big_with_segmenting(self):
n = 150
ham = MPO_ham_heis(n, cyclic=True)
dmrg = DMRG2(ham, bond_dims=range(10, 30, 2))
dmrg.opts['periodic_segment_size'] = 1 / 3
assert dmrg.solve(tol=1, verbosity=2)
assert dmrg.energy == pytest.approx(heisenberg_energy(n), 1e-3)
def test_matches_exact(self, dense, MPO_ham):
h = MPO_ham(6)
dmrg = DMRG2(h, bond_dims=8)
assert dmrg._k.site[0].dtype == float
dmrg.opts['eff_eig_dense'] = dense
assert dmrg.solve()
# XXX: need to dispatch SLEPc seigsys on real input
# assert dmrg._k.site[0].dtype == float
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(mps_gs_dense.H @ mps_gs_dense, 1.0)
h_dense = h.to_dense()
# check against dense form
actual_e, gs = seigsys(h_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
# check against actual MPO_ham
if MPO_ham is MPO_ham_XY:
ham_dense = ham_heis(6, cyclic=False, j=(1.0, 1.0, 0.0))
elif MPO_ham is MPO_ham_heis:
ham_dense = ham_heis(6, cyclic=False)
actual_e, gs = seigsys(ham_dense, k=1)
assert_allclose(actual_e, eff_e)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0)
def test_realistic(self):
seed_rand(42)
ham = MPO_ham_heis(20)
dmrg = DMRG2(ham, bond_dims=[2, 4])
dmrg.solve()
rho_ab = dmrg.state.ptr(range(6, 14))
xf = approx_spectral_function(rho_ab, lambda x: x,
tol=0.1, verbosity=2)
assert_allclose(1.0, xf, rtol=0.6, atol=0.001)
def test_realistic(self):
ham = MPO_ham_heis(20)
dmrg = DMRG2(ham, bond_dims=[4, 8])
dmrg.solve()
sysa, sysb = range(3, 9), range(12, 17)
rho_ab_pt = PTPTLazyMPS(dmrg.state, sysa, sysb)
xf = approx_spectral_function(rho_ab_pt, lambda x: x, beta_tol=1e-6,
tol=0.05, verbosity=2, max_bond=20)
assert_allclose(1, xf, rtol=0.5, atol=0.1)
def test_total_size_2(self):
N = 2
builder = SpinHam(1 / 2)
for i in range(N - 1):
builder[i, i + 1] += 1.0, 'Z', 'Z'
H = builder.build_mpo(N)
dmrg = DMRG2(H)
dmrg.solve(verbosity=1)
assert dmrg.energy == pytest.approx(-1 / 4)
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)
def test_matches_exact(self, dense, MPO_ham, cyclic):
n = 6
h = MPO_ham(n, cyclic=cyclic)
tol = 3e-2 if cyclic else 1e-4
dmrg = DMRG2(h, bond_dims=[4, 8, 12])
assert dmrg._k[0].dtype == float
dmrg.opts['local_eig_ham_dense'] = dense
dmrg.opts['periodic_segment_size'] = 1.0
dmrg.opts['periodic_nullspace_fudge_factor'] = 1e-6
assert dmrg.solve(tol=tol / 10, verbosity=1)
# XXX: need to dispatch SLEPc eigh on real input
# assert dmrg._k[0].dtype == float
eff_e, mps_gs = dmrg.energy, dmrg.state
mps_gs_dense = mps_gs.to_dense()
assert_allclose(expec(mps_gs_dense, mps_gs_dense), 1.0, rtol=tol)
h_dense = h.to_dense()
# check against dense form
actual_e, gs = eigh(h_dense, k=1)
assert_allclose(actual_e, eff_e, rtol=tol)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0, rtol=tol)
# check against actual MPO_ham
if MPO_ham is MPO_ham_XY:
ham_dense = ham_heis(n, cyclic=cyclic, j=(1.0, 1.0, 0.0))
elif MPO_ham is MPO_ham_heis:
ham_dense = ham_heis(n, cyclic=cyclic)
actual_e, gs = eigh(ham_dense, k=1)
assert_allclose(actual_e, eff_e, rtol=tol)
assert_allclose(abs(expec(mps_gs_dense, gs)), 1.0, rtol=tol)