experiments: comparison to Fig. 3a in Bruhat et al. 2018

experiments.py

@@ -112,6 +112,9 @@ def bruhat18_fig2ab(dm, omega, dc_res=100, ac_res=100, vdc_min=0, vac_min=0, vdc
     vac_max = min(vac_max, results.vac.max())
     vdc_max = min(vdc_max, results.vdc.max())
 
+    tk_mueV = 28.2  # Kondo temperature in μeV, defined by G(V=Tk)=e²/h
+    tkrg_mueV = tk_mueV / TK_VOLTAGE # Kondo temperature in μeV defined as integration constant in RTRG
+
     # Interpolate
     #gdc_J_tck   = bisplrep(results.vac[j], results.vdc[j], results.dc_conductance[j], s=2e-6, kx=3, ky=3)
     #idc_J_tck   = bisplrep(results.vac[j], results.vdc[j], results.dc_current[j], s=2e-6, kx=3, ky=3)
@@ -137,18 +140,18 @@ def bruhat18_fig2ab(dm, omega, dc_res=100, ac_res=100, vdc_min=0, vac_min=0, vdc
 
     # Create figure
     fig, ax1 = plt.subplots(1, 1, sharex=True, sharey=True)
-    ax1.set_ylabel("Vac")
-    ax1.set_xlabel("Vdc")
+    ax1.set_ylabel("Vac (μV)")
+    ax1.set_xlabel("Vdc (μV)")
 
     # DC conductance
     gnorm = plt.Normalize(np.pi*results.dc_conductance.min(), np.pi*results.dc_conductance.max())
     cmap = plt.cm.Oranges
     ax1.set_title('DC conductance')
-    #ax1.scatter(results.vdc[j], results.vac[j], c=np.pi*results.dc_conductance[j], marker='x', norm=gnorm, cmap=plt.cm.viridis)
-    #ax1.scatter(results.vdc[mu], results.vac[mu], c=np.pi*results.dc_conductance[mu], marker='+', norm=gnorm, cmap=plt.cm.viridis)
-    img = ax1.imshow(np.pi*gdc_g_mu_interp, extent=(0, vdc_max, 0, vac_max), aspect='auto', cmap=cmap, norm=gnorm, origin='lower')
-    ax1.imshow(np.pi*gdc_g_mu_interp, extent=(0, -vdc_max, 0, vac_max), aspect='auto', cmap=cmap, norm=gnorm, origin='lower')
-    ax1.set_xlim(-vdc_max, vdc_max)
+    #ax1.scatter(tkrg_mueV*results.vdc[j], tkrg_mueV*results.vac[j], c=np.pi*results.dc_conductance[j], marker='x', norm=gnorm, cmap=plt.cm.viridis)
+    #ax1.scatter(tkrg_mueV*results.vdc[mu], tkrg_mueV*results.vac[mu], c=np.pi*results.dc_conductance[mu], marker='+', norm=gnorm, cmap=plt.cm.viridis)
+    img = ax1.imshow(np.pi*gdc_g_mu_interp, extent=(0, vdc_max*tkrg_mueV, 0, vac_max*tkrg_mueV), aspect='auto', cmap=cmap, norm=gnorm, origin='lower')
+    ax1.imshow(np.pi*gdc_g_mu_interp, extent=(0, -vdc_max*tkrg_mueV, 0, vac_max*tkrg_mueV), aspect='auto', cmap=cmap, norm=gnorm, origin='lower')
+    ax1.set_xlim(-tkrg_mueV*vdc_max, tkrg_mueV*vdc_max)
     fig.colorbar(img, ax=ax1)
 
 def bruhat18_fig2c(dm, **kwargs):
@@ -264,6 +267,33 @@ def kogan04_calibrate(dm, **kwargs):
 
     return fig, ax
 
+def bruhat18_fig3a(dm, omega_res=100, vac_res=100, **kwargs):
+    for name in ("omega", "vdc", "vac"):
+        kwargs.pop(name, None)
+    results = dm.list(vdc=0, **kwargs)
+    results = results.loc[(results.vac < 15) & np.isfinite(results.dc_conductance)]
+
+    omega_arr = np.linspace(0.8, 10, omega_res) # units of Tkrg
+    vac_arr = np.linspace(0.1, 12, vac_res) # units of Tkrg
+
+    #tk_mueV = 28.2  # Kondo temperature in μeV, defined by G(V=Tk)=e²/h
+    #tkrg_mueV = tk_mueV / TK_VOLTAGE # Kondo temperature in μeV defined as integration constant in RTRG
+
+    fig, ax = plt.subplots()
+    ax.set_xlabel("Ω (Tk)")
+    ax.set_ylabel("Vac (Tk)")
+    gdc_tck = bisplrep(results.omega, results.vac, results.dc_conductance, s=1e-4, kx=3, ky=3)
+    gdc_interp = bisplev(omega_arr, vac_arr, gdc_tck).T
+
+    img = ax.imshow(
+            np.pi*gdc_interp,
+            extent = ((0.8-4.6/omega_res)/TK_VOLTAGE, (10+4.6/omega_res)/TK_VOLTAGE, (0.1-5.95/vac_res)/TK_VOLTAGE, (12+5.95/vac_res)/TK_VOLTAGE),
+            aspect = 'auto',
+            cmap = plt.cm.jet,
+            origin='lower')
+    ax.scatter(results.omega/TK_VOLTAGE, results.vac/TK_VOLTAGE, c=np.pi*results.dc_conductance, cmap=img.cmap, norm=img.norm)
+    fig.colorbar(img, ax=ax)
+    return fig, ax
 
 def plot_calibration_lines(
         dm,

gen_data.py

@@ -301,7 +301,7 @@ python -m frtrg_kondo.gen_data \\
         dm = DataManager()
         for kondo_options in gen_option_iter(**options):
             vdc = kondo_options['vdc'] + kondo_options['omega']*kondo_options['resonant_dc_shift']
-            settings.logger.info(f"Vdc={vdc}, Vac={kondo_options['vac']}, Ω={kondo_options['omega']}")
+            settings.logger.info(f"Starting with Vdc={vdc}, Vac={kondo_options['vac']}, Ω={kondo_options['omega']}")
             kondo = Kondo(**kondo_options)
             kondo.run(**solver_options)
             settings.logger.info(f"Saving Vdc={vdc}, Vac={kondo_options['vac']}, Ω={kondo_options['omega']} to {filename}")

kondo.py

@@ -368,13 +368,13 @@ class Kondo:
                 Handle with care!
                 valid values: padding + clear_corners <= 2*nmax + 1
         compact : Use extra symmetry to improve efficiency for large matrices.
-                compact != 0 requires the symmetry V(t+(π/Ω)) = - V(t).
-                valid values are:
+                compact != 0 requires unitary_transformation==True and the
+                symmetry V(t+(π/Ω)) = - V(t). Valid values are:
                     0: don't use compact form.
                     1: compact form that ignores matrix elements which are zero
                         by symmetry
                     2: compact form which additionally uses symmetry of the
-                        nonzero matrix elements
+                        nonzero matrix elements. requires xL = 0.5.
         '''
         self.global_properties = GlobalRGproperties(
                 nmax = nmax,
@@ -410,7 +410,6 @@ class Kondo:
             assert self.vdc == omega*resonant_dc_shift
             assert fourier_coef is None or np.allclose(fourier_coef[1::2], 0)
             assert self.resonant_dc_shift == 0 # extending the implementation to allow for even resonant_dc_shift requires some checks, odd resonant_dc_shift require some rewriting.
-            assert self.padding % 2 == 0
         assert d.imag == 0.
         self.d = d