diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 6f82746d..26918807 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -19,7 +19,8 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1'
+          - 'lts' # minimal supported version
+          - '1' # latest released Julia version
         os:
           - ubuntu-latest
           - macOS-latest
diff --git a/src/utility/cft.jl b/src/utility/cft.jl
index 2258e14e..258fd6e6 100644
--- a/src/utility/cft.jl
+++ b/src/utility/cft.jl
@@ -76,7 +76,7 @@ end
 function area_term(A, B; is_real = true)
     a_in = domain(A)[1]
     b_in = domain(B)[1]
-    x0 = rand(a_in ⊗ b_in)
+    x0 = ones(a_in ⊗ b_in)
 
     function f0(x)
         @plansor fx[-1 -2] := A[c -1; 1 m] * x[1 2] * B[m -2; 2 c]
@@ -84,8 +84,10 @@ function area_term(A, B; is_real = true)
         return ffx
     end
 
-    spec0, _, _ = eigsolve(f0, x0, 1, :LR; verbosity = 0)
-
+    spec0, _, info = eigsolve(f0, x0, 1, :LR; verbosity = 0)
+    if info.converged == 0
+        @warn "The area term eigensolver did not converge."
+    end
     if is_real
         return real(spec0[1])
     else
@@ -176,15 +178,18 @@ function spec(TA::TensorMap, TB::TensorMap, shape::Array; Nh = 25)
     spec_sector = Dict(
         map(sectors(fuse(xspace))) do charge
             V = (I == Trivial) ? 𝔽^1 : Vect[I](charge => 1)
-            x = rand(xspace ← V)
+            x = ones(xspace ← V)
             if dim(x) == 0
                 return charge => [0.0]
             else
-                spec, _, _ = eigsolve(
+                spec, _, info = eigsolve(
                     a -> f(TA, TB, a), x, Nh, :LM; krylovdim = 40, maxiter = 100,
                     tol = 1.0e-12,
                     verbosity = 0
                 )
+                if info.converged == 0
+                    @warn "The spectrum eigensolver in sector $charge did not converge."
+                end
                 return charge => filter(x -> abs(real(x)) ≥ 1.0e-12, spec)
             end
         end
diff --git a/test/schemes.jl b/test/schemes.jl
index 4d86cf8f..7f5aa78c 100644
--- a/test/schemes.jl
+++ b/test/schemes.jl
@@ -91,9 +91,8 @@ end
     @info "LoopTNR ising free energy"
     scheme = LoopTNR(T)
 
-    entanglement_function(steps, data) = abs(data[end])
-    entanglement_criterion = maxiter(100) & convcrit(1.0e-15, entanglement_function)
-    loop_criterion = maxiter(5) & convcrit(1.0e-10, entanglement_function)
+    entanglement_criterion = maxiter(100)
+    loop_criterion = maxiter(5)
 
     data = run!(
         scheme, truncdim(8), truncbelow(1.0e-12), maxiter(25), entanglement_criterion,
@@ -104,22 +103,22 @@ end
 
     @info "LoopTNR ising CFT data"
     scheme = LoopTNR(T)
-    run!(scheme, truncdim(8), maxiter(10))
+    run!(scheme, truncdim(12), maxiter(10))
 
     for shape in [[1, 4, 1], [sqrt(2), 2 * sqrt(2), 0]]
         cft = cft_data!(scheme, shape)
         d1, d2 = real(cft[Z2Irrep(1)][1]), real(cft[Z2Irrep(0)][2])
         @info "Obtained lowest scaling dimensions:\n$(d1), $(d2)."
         @test d1 ≈ ising_cft_exact[1] rtol = 5.0e-4
-        @test d2 ≈ ising_cft_exact[2] rtol = 1.0e-2
+        @test d2 ≈ ising_cft_exact[2] rtol = 5.0e-4
     end
 
     for shape in [[1, 8, 1], [4 / sqrt(10), 2 * sqrt(10), 2 / sqrt(10)]]
-        cft = cft_data!(scheme, shape, truncdim(8), truncbelow(1.0e-10))
+        cft = cft_data!(scheme, shape, truncdim(12), truncbelow(1.0e-10))
         d1, d2 = real(cft[Z2Irrep(1)][1]), real(cft[Z2Irrep(0)][2])
         @info "Obtained lowest scaling dimensions:\n$(d1), $(d2)."
-        @test d1 ≈ ising_cft_exact[1] rtol = 1.0e-2
-        @test d2 ≈ ising_cft_exact[2] rtol = 1.0e-2
+        @test d1 ≈ ising_cft_exact[1] rtol = 1.0e-3
+        @test d2 ≈ ising_cft_exact[2] rtol = 1.0e-3
     end
 end