tests: fixup prefactors

tests/test_solver.py

@@ -270,7 +270,7 @@ def test_soc_analytic(n=10):
     sz = np.array([[1, 0], [0, -1]])
     s0 = np.array([[1, 0], [0, 1]])
 
-    def get_sol(soc_alpha, alpha, L=10, h=0.5):
+    def get_sol(soc_alpha, alpha, L=10, h=0.5, D=1.0):
         sol = Solver(nx=n, ny=n)
         sol.mask[...] = MASK_NONE
         sol.Lx = L
@@ -279,6 +279,7 @@ def test_soc_analytic(n=10):
         sol.Omega[...] = 0
         sol.Delta[:, :] = np.eye(2)
 
+        sol.D = D
         sol.alpha = alpha
 
         nx, ny = sol.shape
@@ -295,10 +296,16 @@ def test_soc_analytic(n=10):
 
         return sol
 
-    sol = get_sol(soc_alpha=1.0, alpha=1.0)
-    sol0 = get_sol(soc_alpha=0, alpha=0)
+    # Solver without SOC
+    h = 0.5
+    sol0 = get_sol(soc_alpha=0, alpha=0, h=h)
 
-    T = 0.2
+    # Solver for evaluating current perturbatively in SOC
+    alpha_soc = 0.01
+    alpha = 1.0
+    sol = get_sol(soc_alpha=alpha_soc, alpha=alpha, h=h, D=0)
+
+    T = 0.4
     E_typical = 10 + 10 * T
     w, a = get_matsubara_sum(T, E_typical)
 
@@ -308,18 +315,35 @@ def test_soc_analytic(n=10):
     Fs = []
     Gs = []
     Js = []
+    Jans = []
+
+    dd = (sol.Lx / sol.shape[0], sol.Ly / sol.shape[1])
 
     Jtot = 0
+    Jantot = 0
     for ww, aa in zip(w, a):
-        res0 = sol0.solve(omega=ww, finite_difference=False)
+        res0 = sol0.solve(omega=ww)
         sol.omega = ww
-        J = sol._core.grad_A(res0.Phi.copy()).transpose(0, 1, 2, 4, 3) * (-1 / 8)
-
+        J = sol._core.grad_A(res0.Phi.copy()).transpose(0, 1, 2, 4, 3) * (1 / 16)
+        J[:, :, 0] /= dd[1] * sol.Ly
+        J[:, :, 1] /= dd[0] * sol.Lx
+        J[:, :, 2] /= dd[1] * sol.Ly
+        J[:, :, 3] /= dd[0] * sol.Lx
         Jtot += aa * J
 
+        gp = (ww - 1j * h) / np.sqrt((ww - 1j * h) ** 2 + 1)
+        gm = (ww + 1j * h) / np.sqrt((ww + 1j * h) ** 2 + 1)
+        fp = 1 / np.sqrt((ww - 1j * h) ** 2 + 1)
+        fm = 1 / np.sqrt((ww + 1j * h) ** 2 + 1)
+        Jy_an = (
+            (gp - gm) * (1 + gp * gm + fp * fm) * (-1j * pi * alpha * alpha_soc**3)
+        )
+        Jantot += aa * Jy_an
+
         Fs.append(res0.F.copy())
         Gs.append(res0.G.copy())
         Phis.append(res0.Phi.copy())
         Js.append(J)
+        Jans.append(Jy_an)
 
     return locals()