diff --git a/data_management.py b/data_management.py
index e28ad52822cb4b64c510667aafa262886e66750d..a8841d01b1e89e87d6c85446a63fe3a86812cb70 100644
--- a/data_management.py
+++ b/data_management.py
@@ -145,6 +145,11 @@ class KondoExport:
solver_flags |= DataManager.SOLVER_FLAGS["simplified_initial_conditions"]
except AttributeError:
pass
+ try:
+ if self.kondo.improved_initial_conditions:
+ solver_flags |= DataManager.SOLVER_FLAGS["improved_initial_conditions"]
+ except AttributeError:
+ pass
try:
if self.kondo.include_Ga:
solver_flags |= DataManager.SOLVER_FLAGS["include_Ga"]
@@ -655,6 +660,7 @@ class DataManager:
second_order_rg_equations = 0x0400,
solve_integral_exactly = 0x0800,
include_Ga = 0x1000,
+ improved_initial_conditions = 0x2000,
)
def __init__(self):
diff --git a/gen_data.py b/gen_data.py
index b9abb0c9080d9362ca0ba8ac8d9e311f1f920724..be69e3e9358b61d16ea5b4d7e8e4e9ab87626372 100644
--- a/gen_data.py
+++ b/gen_data.py
@@ -241,8 +241,11 @@ python -m frtrg_kondo.gen_data \\
method_group.add_argument("--method", type=str, required=True, choices=('J', 'mu'),
help = "J: include all time dependence in coupling by unitary transformation.\nmu: describe time dependence by Floquet matrix for chemical potentials.")
method_group.add_argument("--simplified_initial_conditions", metavar="bool",
- type=bool, default=False,
+ type=int, default=0,
help = "Set initial condition for gammaL to 0")
+ method_group.add_argument("--improved_initial_conditions", metavar="bool",
+ type=int, default=0,
+ help = "Set initial condition for dgammaL/dE to linear response estimate")
method_group.add_argument("--include_Ga", metavar="int", type=int,
default=1, choices=(0,1),
help = "include vertex parameter Ga in RG equations")
diff --git a/kondo.py b/kondo.py
index 8d785b6e0639797e049cc07a43b3cfd90aa8b879..ee5eaef3e9c4474835629830e36b1a14debbda6b 100644
--- a/kondo.py
+++ b/kondo.py
@@ -462,6 +462,7 @@ class Kondo:
xL : 'asymmetry factor' = 0.5,
compact = 0,
simplified_initial_conditions = False,
+ improved_initial_conditions = False,
truncation_order = 3,
**rg_properties):
"""
@@ -510,6 +511,8 @@ class Kondo:
simplified_initial_conditions : use simplified initial
conditions for the current kernel which lead to the same
result in the limit of large D.
+ improved_initial_conditions : use nonzero initial condition for
+ derivative of current kernel Γ^L
truncation_order : Truncation order of RG equations, must be 2 or 3.
"""
self.global_properties = GlobalRGproperties(
@@ -528,6 +531,8 @@ class Kondo:
self.global_settings = settings.export()
self.unitary_transformation = unitary_transformation
self.simplified_initial_conditions = simplified_initial_conditions
+ self.improved_initial_conditions = improved_initial_conditions
+ assert not (simplified_initial_conditions and improved_initial_conditions)
self.include_Ga = include_Ga
self.solve_integral_exactly = solve_integral_exactly
if truncation_order == 2:
@@ -737,9 +742,18 @@ class Kondo:
np.zeros((2*self.nmax+1,2*self.nmax+1), dtype=np.complex128),
symmetry = -symmetry
)
+ mu_matrix = self.mu.reduced(shift=1)
+ if self.improved_initial_conditions:
+ gamma = gamma0[self.voltage_branches].diagonal()
+ j = j0[self.voltage_branches].diagonal()
+ z = z0[self.voltage_branches].diagonal()
+ ddGammaL = 12j*np.pi*self.xL*(1-self.xL) * j**3/(self.d+gamma)
+ if self.truncation_order >= 3:
+ ddGammaL *= z**2*(1-z*j)
+ self.yL = RGfunction(self.global_properties, mu_matrix.values * ddGammaL.reshape((1,-1)), symmetry=-symmetry)
### Full current, also includes AC current
- self.gammaL = self.mu.reduced(shift=1) @ self.deltaGammaL
+ self.gammaL = mu_matrix @ self.deltaGammaL
if self.simplified_initial_conditions:
self.gammaL *= 0
@@ -791,6 +805,11 @@ class Kondo:
zj0 = z0 * j0 if self.truncation_order >= 3 else j0
zjvalues = zvalues * jvalues if self.truncation_order >= 3 else jvalues
+ gamma0_red = gamma0[self.voltage_branches] if self.voltage_branches else gamma0
+ z0_red = z0[self.voltage_branches] if self.voltage_branches else z0
+ j0_red = j0[self.voltage_branches] if self.voltage_branches else j0
+ zj0_red = zj0[self.voltage_branches] if self.voltage_branches else zj0
+
RGclass = SymRGfunction if self.compact else RGfunction
# Create Γ and Z with the just calculated initial values.
@@ -912,16 +931,10 @@ class Kondo:
self.current[0,0].symmetry = -symmetry
self.current[1,1] = self.current[0,0].copy()
if self.vac or self.resonant_dc_shift or self.fourier_coef is not None:
- if self.voltage_branches:
- if self.truncation_order >= 3:
- i0 = j0[self.voltage_branches] * (1 - zj0[self.voltage_branches])
- else:
- i0 = j0[self.voltage_branches]
+ if self.truncation_order >= 3:
+ i0 = j0_red * (1 - zj0_red)
else:
- if self.truncation_order >= 3:
- i0 = j0 * (1 - zj0)
- else:
- i0 = j0
+ i0 = j0_red
i_LR = np.einsum(
'ij,...j->...ij',
init_matrix,
@@ -968,17 +981,10 @@ class Kondo:
)
if self.resonant_dc_shift:
assert self.compact == 0
- if self.voltage_branches:
- self.deltaGammaL.values[diag_idx] = 3*np.pi*self.xL*(1-self.xL) \
- * zj0[self.voltage_branches,self.resonant_dc_shift:-self.resonant_dc_shift]**2
- else:
- self.deltaGammaL.values[diag_idx] = 3*np.pi*self.xL*(1-self.xL) \
- * zj0[self.resonant_dc_shift:-self.resonant_dc_shift]**2
+ self.deltaGammaL.values[diag_idx] = 3*np.pi*self.xL*(1-self.xL) \
+ * zj0_red[self.resonant_dc_shift:-self.resonant_dc_shift]**2
else:
- if self.voltage_branches:
- diag_values = 3*np.pi*self.xL*(1-self.xL) * zj0[self.voltage_branches]**2
- else:
- diag_values = 3*np.pi*self.xL*(1-self.xL) * zj0**2
+ diag_values = 3*np.pi*self.xL*(1-self.xL) * zj0_red**2
if self.compact:
assert diag_values.dtype == np.complex128
self.deltaGammaL.submatrix00 = np.diag(diag_values[0::2])
@@ -1018,19 +1024,39 @@ class Kondo:
mu[np.arange(i, 2*self.nmax+1), np.arange(2*self.nmax+1-i)] = f.conjugate()
mu = RGclass(self.global_properties, mu, symmetry=1)
self.gammaL = mu @ self.deltaGammaL.reduced()
+ if self.improved_initial_conditions:
+ ddGammaL = 12j*np.pi*self.xL*(1-self.xL) * j0_red**3/(self.d+gamma0_red)
+ if self.truncation_order >= 3:
+ ddGammaL *= z0_red**2*(1-z0_red*j0_red)
+ if self.compact:
+ self.yL = SymRGfunction(self.global_properties, mu.values * ddGammaL.reshape((1,-1)), symmetry=-symmetry, diag=False, offdiag=True)
+ else:
+ self.yL = RGfunction(self.global_properties, mu.values * ddGammaL.reshape((1,-1)), symmetry=-symmetry)
else:
self.gammaL = self.vdc * self.deltaGammaL.reduced()
- if self.vac and self.fourier_coef is None:
- if self.voltage_branches:
- gammaL_AC = 3*np.pi*self.xL*(1-self.xL) * self.vac/2 * zj0[self.voltage_branches]**2
+ if self.improved_initial_conditions and self.vdc:
+ if self.truncation_order >= 3:
+ self.yL.values += np.diag(self.vdc * 12j*np.pi*self.xL*(1-self.xL) * j0_red**3*z0_red**2*(1-z0_red*j0_red)/(self.d+gamma0_red))
else:
- gammaL_AC = 3*np.pi*self.xL*(1-self.xL) * self.vac/2 * zj0**2
+ self.yL.values += np.diag(self.vdc * 12j*np.pi*self.xL*(1-self.xL) * j0_red**3/(self.d+gamma0_red))
+ if self.vac and self.fourier_coef is None:
+ gammaL_AC = 3*np.pi*self.xL*(1-self.xL) * self.vac/2 * zj0_red**2
if self.resonant_dc_shift:
gammaL_AC = gammaL_AC[...,self.resonant_dc_shift:-self.resonant_dc_shift]
idx = (np.arange(1, 2*self.nmax+1), np.arange(2*self.nmax))
self.gammaL.values[idx] = gammaL_AC[...,1:]
idx = (np.arange(0, 2*self.nmax), np.arange(1, 2*self.nmax+1))
self.gammaL.values[idx] = gammaL_AC[...,:-1]
+ if self.improved_initial_conditions:
+ yL_AC = 12j*np.pi*self.xL*(1-self.xL) * self.vac/2 * j0_red**3/(self.d+gamma0_red)
+ if self.truncation_order >= 3:
+ yL_AC *= z0_red**2*(1-z0_red*j0_red)
+ if self.resonant_dc_shift:
+ yL_AC = yL_AC[...,self.resonant_dc_shift:-self.resonant_dc_shift]
+ idx = (np.arange(1, 2*self.nmax+1), np.arange(2*self.nmax))
+ self.yL.values[idx] = yL_AC[...,1:]
+ idx = (np.arange(0, 2*self.nmax), np.arange(1, 2*self.nmax+1))
+ self.yL.values[idx] = yL_AC[...,:-1]
if self.simplified_initial_conditions:
self.gammaL *= 0
diff --git a/settings.py b/settings.py
index 81f8e9d9c4e5fab475e391f061a9d069bda2ecdb..f9d8017242a4668074eda7f8ac7322c8135ad872 100644
--- a/settings.py
+++ b/settings.py
@@ -86,7 +86,7 @@ class GlobalFlags:
BASEPATH = os.path.abspath("data"),
DB_CONNECTION_STRING = "sqlite:///" + os.path.join(os.path.abspath("data"), "frtrg.sqlite"),
FILENAME = "frtrg-04.h5",
- VERSION = (14, 15, -1, -1),
+ VERSION = (14, 16, -1, -1),
MIN_VERSION = (14, 0),
LOG_TIME = 10, # in s
ENFORCE_SYMMETRIC = 0,