def perform_imaginary_time_evolution_1D(J):
if J == 0.15:
E_expected = -3.9412627297
elif J == 0.05:
E_expected = -3.317526309839
else:
sys.exit('ERROR: test_imaginary_time_evolution_1D called with J=%s.' %
J)
G = Gutzwiller(seed=12311123,
J=J,
U=1.0,
D=1,
mu=0.5,
L=19,
VT=0.02,
alphaT=2,
nmax=4,
OBC=1)
G.many_time_steps(0.5j,
nsteps=1000,
normalize_at_each_step=1,
update_variables=0)
print('J/U: %s' % (G.J / G.U))
print('E: %.12f' % G.E)
print('E: %.12f (expexted)' % E_expected)
print()
assert abs(G.E - E_expected) < 1e-4
def test_neighbors_reciprocity():
for OBC in [0, 1]:
for D in [1, 2]:
for L in [5, 10]:
G = Gutzwiller(D=D, L=L, OBC=OBC)
for i_site in range(G.N_sites):
for j_nbr in range(G.N_nbr[i_site]):
j_site = G.nbr[i_site, j_nbr]
assert i_site in list(G.nbr[j_site, :])
def test_bisection_to_find_mu():
Ntarget = 10.0
tol = 0.1
G = Gutzwiller(J=0.05,
U=1.0,
D=1,
mu=0.0,
L=15,
VT=0.05,
alphaT=2,
nmax=4,
OBC=1)
n_iterations = G.set_mu_via_bisection(Ntarget=Ntarget,
mu_min=-0.5,
mu_max=1.5,
tol_N=tol)
print('#iterations: %i' % n_iterations)
print('Ntarget: %f' % Ntarget)
print('G.mu: %.8f (N=%f)' % (G.mu, G.N))
assert (G.N - Ntarget) < tol
def test_lattice_definition_2D():
xy = numpy.empty(2, dtype=numpy.int32)
for L in [2, 3, 10, 11]:
G = Gutzwiller(D=2, L=L)
for i_site in range(G.N_sites):
x, y = G.site_coords[i_site, :]
assert i_site == G.xy2i(x, y)
for x, y in itertools.product(range(L), repeat=2):
i_site = G.xy2i(x, y)
G.i2xy(i_site, xy)
assert x == xy[0]
assert y == xy[1]
OBC = 0 # Whether to impose open (OBC=1) or periodic (OBC=0) boundary conditions
VT = 0.0 # Trap prefactor, as in V(r) = VT * r^alpha
alphaT = 0.0 # Trap exponent, as in V(r) = VT * r^alpha
# Parameters for the bisection algorithm (that is, to look for the chemical potential giving the right number of particles)
Ntarget = 17 # Expected number of particles
tol_N = 0.01 # Tolerance on the average N
mu_min = 0.0 # The bisection algorithm will search the optimal chemical potential in the interval [mu_min, mu_max]
mu_max = 2.0 # The bisection algorithm will search the optimal chemical potential in the interval [mu_min, mu_max]
# Initialize the state
G = Gutzwiller(seed=12312311,
J=J,
U=U,
mu=-20.0,
D=D,
L=L,
VT=VT,
alphaT=alphaT,
nmax=nmax,
OBC=OBC)
# Perform bisection to find the right chemical potential
n_iterations = G.set_mu_via_bisection(Ntarget=Ntarget,
mu_min=mu_min,
mu_max=mu_max,
tol_N=tol_N)
print()
print('Final chemical potential: mu/U = %.6f' % (G.mu / G.U))
print('Final number of particles: E/U = %.6f' % G.N)
print('Final density: <n> = %.6f' % np.mean(G.density))
nmax = 4 # Cutoff on the local occupation
OBC = 1 # Whether to impose open (OBC=1) or periodic (OBC=0) boundary conditions
VT = 0.2 # Trap prefactor, as in V(r) = VT * r^alpha
alphaT = 2.0 # Trap exponent, as in V(r) = VT * r^alpha
mu = 1.2 # Chemical potential
# Parameters for imaginary-time evolution
dt = 0.1 / J # Time interval, in units of
nsteps = 300 # Number of time-evolution steps
# Initialize the state
G = Gutzwiller(seed=12312311,
J=J,
U=U,
mu=mu,
D=D,
L=L,
VT=VT,
alphaT=alphaT,
nmax=nmax,
OBC=OBC)
# Imaginary-time dynamics
G.many_time_steps(1.0j * dt, nsteps=nsteps)
# Print some output and save the density profile
print('End of ground-state search (via imaginary-time evolution)')
print('Chemical potential: mu/U = %.6f' % (G.mu / G.U))
print('Final number of particles: E/U = %.6f' % G.N)
print('Final density: <n> = %.6f' % numpy.mean(G.density))
print('Final energy: E/U = %.6f' % (G.E / G.U))
print()
U = 0.2 # On-site repulsion
J = 1.0 # Hopping amplitude
mu = -0.49260342 # Chemical potential
nmax = 32 # Cutoff on the local occupation
OBC = 1 # Open (OBC=1) or periodic (OBC=0) boundary conditions
Ntarget = 20 # Target number of particles
VT = 0.3 * J # Trap prefactor, as in V(r) = VT * r^alpha
alphaT = 2.0 # Trap exponent, as in V(r) = VT * r^alpha
# Initialize the state
G = Gutzwiller(seed=12312311,
J=J,
U=U,
mu=mu,
D=D,
L=L,
VT=VT,
alphaT=alphaT,
nmax=nmax,
OBC=OBC)
# Find ground state via imaginary-time dynamics
dt = 0.1 / J # Time interval
nsteps = 200 # Number of time-evolution steps
G.many_time_steps(1.0j * dt, nsteps=nsteps)
# Print some output and save the density profile
G.save_densities('data_ex5_densities_pre_quench.dat')
print()
print('End of initial-state preparation (via imaginary-time dynamics)')
print('Chemical potential: mu/U = %.8f, mu/J = %.8f' %
OBC = 0 # Whether to impose open (OBC=1) or periodic (OBC=0) boundary conditions
VT = 0.0 # Trap prefactor, as in V(r) = VT * r^alpha
alphaT = 0.0 # Trap exponent, as in V(r) = VT * r^alpha
mu = 1.2 # Chemical potential
# Parameters for imaginary-time evolution
dt = 0.1 / J # Time interval, in units of
nsteps = 200 # Number of time-evolution steps
# Initialize the state
G = Gutzwiller(seed=12312311,
J=J,
U=U,
mu=mu,
D=D,
L=L,
Vnn=Vnn,
VT=VT,
alphaT=alphaT,
nmax=nmax,
OBC=OBC)
G.print_parameters()
# Imaginary-time dynamics
G.many_time_steps(1.0j * dt, nsteps=nsteps)
print('Optimization completed')
print('Number of particles: <N> = %.6f' % G.N)
print('Energy: E/U = %.6f' % (G.E / G.U))
print('Densities:')
for i_site in range(G.N_sites):
print(' site %2i, n=%.6f' % (i_site, G.density[i_site]))