diff --git a/src/schemes/symmetric_looptnr.jl b/src/schemes/symmetric_looptnr.jl
index cecc436b..9b4d9bbc 100644
--- a/src/schemes/symmetric_looptnr.jl
+++ b/src/schemes/symmetric_looptnr.jl
@@ -23,15 +23,16 @@ $(TYPEDFIELDS)
 """
 mutable struct SLoopTNR <: TNRScheme
     T::TensorMap
+    S::TensorMap
 
     gradalg::OptimKit.LBFGS
     finalize!::Function
     function SLoopTNR(
-            T::TensorMap;
-            gradalg = LBFGS(10; verbosity = 0, gradtol = 6.0e-7, maxiter = 40000),
-            finalize = (finalize!)
-        )
-        return new(T, gradalg, finalize)
+        T::TensorMap;
+        gradalg = LBFGS(10; verbosity = 0, gradtol = 6.0e-7, maxiter = 40000),
+        finalize = (finalize!),
+    )
+        return new(T, T, gradalg, finalize)
     end
 end
 
@@ -42,8 +43,8 @@ function classical_ising_inv(β)
 
     S = ℤ₂Space(0 => 1, 1 => 1)
     T = zeros(Float64, S ⊗ S ← S' ⊗ S')
-    block(T, Irrep[ℤ₂](0)) .= [2x^2 2x * y; 2x * y 2y^2]
-    block(T, Irrep[ℤ₂](1)) .= [2x * y 2x * y; 2x * y 2x * y]
+    block(T, Irrep[ℤ₂](0)) .= [2x^2 2x*y; 2x*y 2y^2]
+    block(T, Irrep[ℤ₂](1)) .= [2x*y 2x*y; 2x*y 2x*y]
 
     return permute(T, (1, 2, 3, 4))
 end
@@ -77,14 +78,17 @@ function TTtoNorm(TT)
     return tr(T8 * b)
 end
 
-function cost_looptnr(S, T)
+function to_const_TT(T)
+    @tensor TT[-1 -2; -3 -4] := T[1 -1 2 -3] * conj(T[1 -2 2 -4])
+    return TTtoNorm(TT)
+end
+
+function cost_looptnr(S, T, const_TT)
     @assert eltype(S) == Float64 "Modification is needed for complex numbers!"
     SS = StoSS(S)
-    @tensor TT[-1 -2; -3 -4] := T[1 -1 2 -3] * conj(T[1 -2 2 -4])
     @tensor TSS[-1 -2; -3 -4] := T[1 -1 2 -3] * conj(SS[1 -2 2 -4])
     @tensor S4[-1 -2; -3 -4] := SS[1 -1 2 -3] * conj(SS[1 -2 2 -4])
-    # T
-    return TTtoNorm(TT) + TTtoNorm(S4) - 2 * TTtoNorm(TSS)
+    return (const_TT + TTtoNorm(S4) - 2 * TTtoNorm(TSS)) / const_TT
 end
 
 ########## Gradient Optimization ##########
@@ -95,12 +99,10 @@ function fg(f, A)
 end
 
 function optimize_S(scheme, S)
-    opt_fun(x) = cost_looptnr(x, scheme.T)
+    const_TT = to_const_TT(scheme.T)
+    opt_fun(x) = cost_looptnr(x, scheme.T, const_TT)
     opt_fg(x) = fg(opt_fun, x)
-    Sopt, fx, gx, numfg, normgradhistory = optimize(
-        opt_fg, S,
-        scheme.gradalg
-    )
+    Sopt, fx, gx, numfg, normgradhistory = optimize(opt_fg, S, scheme.gradalg)
     return Sopt
 end
 
@@ -127,30 +129,35 @@ function Ψ_corner(T)
     return psi
 end
 
-function entanglement_filtering(T; trunc = truncbelow(1.0e-12))
+function entanglement_filtering(T; ef_trunc = truncbelow(1.0e-14))
     entanglement_function(steps, data) = abs(data[end])
     entanglement_criterion = maxiter(100) & convcrit(1.0e-12, entanglement_function)
 
     psi_center = Ψ_center(T)
     psi_corner = Ψ_corner(T)
 
-    PR_list, PL_list = TNRKit.find_projectors(
-        psi_center, [1, 1, 1, 1], [3, 3, 3, 3],
-        entanglement_criterion, trunc
+    PR_list, PL_list = find_projectors(
+        psi_center,
+        [1, 1, 1, 1],
+        [3, 3, 3, 3],
+        entanglement_criterion,
+        ef_trunc,
     )
     P_bottom = PL_list[1]
     P_right = PL_list[1]
 
-    PR_list, PL_list = TNRKit.find_projectors(
+    PR_list, PL_list = find_projectors(
         psi_corner,
-        [1, 1, 1, 1], [3, 3, 3, 3],
-        entanglement_criterion, trunc
+        [1, 1, 1, 1],
+        [3, 3, 3, 3],
+        entanglement_criterion,
+        ef_trunc,
     )
     P_top = PL_list[3]
     P_left = PL_list[3]
 
-    @tensor T_new[-1 -2 -3 -4] := T[1 2 3 4] * P_left[-1; 1] * P_bottom[-2; 2] *
-        P_top[-3; 3] * P_right[-4; 4]
+    @tensor T_new[-1 -2 -3 -4] :=
+        T[1 2 3 4] * P_left[-1; 1] * P_bottom[-2; 2] * P_top[-3; 3] * P_right[-4; 4]
     return T_new
 end
 
@@ -164,7 +171,7 @@ function ef_oneloop(T, trunc::TensorKit.TruncationScheme)
     ΨA = Ψ_center(T)
     ΨB = []
 
-    for i in 1:4
+    for i = 1:4
         s1, s2 = SVD12(ΨA[i], truncdim(trunc.dim * 2))
         push!(ΨB, s1)
         push!(ΨB, s2)
@@ -173,14 +180,16 @@ function ef_oneloop(T, trunc::TensorKit.TruncationScheme)
     ΨB_function(steps, data) = abs(data[end])
     criterion = maxiter(100) & convcrit(1.0e-12, ΨB_function)
     PR_list, _ = find_projectors(
-        ΨB, [1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2, 2],
-        criterion, trunc
+        ΨB,
+        [1, 1, 1, 1, 1, 1, 1, 1],
+        [2, 2, 2, 2, 2, 2, 2, 2],
+        criterion,
+        trunc,
     )
 
     ΨB_disentangled = []
-    for i in 1:1
-        @tensor B1[-2 -1; -3] := ΨB[i][-1; -2 2] *
-            PR_list[mod(i, 8) + 1][2; -3]
+    for i = 1:1
+        @tensor B1[-2 -1; -3] := ΨB[i][-1; -2 2] * PR_list[mod(i, 8)+1][2; -3]
         push!(ΨB_disentangled, B1)
     end
     S = ΨB_disentangled[1]
@@ -195,8 +204,8 @@ function combine_4S(S)
 end
 
 ########## Main funcitons ##########
-function step!(scheme, trunc, oneloop)
-    scheme.T = entanglement_filtering(scheme.T)
+function step!(scheme, trunc, oneloop; ef_trunc = truncbelow(1.0e-14))
+    scheme.T = entanglement_filtering(scheme.T; ef_trunc)
     if oneloop == true
         S = ef_oneloop(scheme.T, trunc)
     else
@@ -204,14 +213,19 @@ function step!(scheme, trunc, oneloop)
     end
     S = optimize_S(scheme, S)
     scheme.T = combine_4S(S)
+    scheme.S = S
     return scheme
 end
 
 function run!(
-        scheme::SLoopTNR, trscheme::TensorKit.TruncationScheme,
-        criterion::TNRKit.stopcrit; finalize_beginning = true, oneloop = true,
-        verbosity = 1
-    )
+    scheme::SLoopTNR,
+    trscheme::TensorKit.TruncationScheme,
+    criterion::TNRKit.stopcrit;
+    finalize_beginning = true,
+    oneloop = true,
+    verbosity = 1,
+    ef_trunc = truncbelow(1.0e-14),
+)
     data = []
 
     LoggingExtras.withlevel(; verbosity) do
@@ -225,7 +239,7 @@ function run!(
 
         t = @elapsed while crit
             @infov 2 "Step $(steps + 1), data[end]: $(!isempty(data) ? data[end] : "empty")"
-            step!(scheme, trscheme, oneloop)
+            step!(scheme, trscheme, oneloop; ef_trunc)
             push!(data, scheme.finalize!(scheme))
             steps += 1
             crit = criterion(steps, data)