Improve CTMRG error computation (QuantumKitHub#65)

* Add non-fixedspace error calculation

* Refactor error calculation

src/algorithms/ctmrg/gaugefix.jl

@@ -139,22 +139,32 @@ function fix_global_phases(envprev::CTMRGEnv, envfix::CTMRGEnv)
     return CTMRGEnv(cornersgfix, edgesgfix)
 end
 
+#=
+In order to compute an error measure, we compare the singular values of the current iteration with the previous one.
+However, when the virtual spaces change, this comparison is not directly possible.
+Instead, we project both tensors into the smaller space and then compare the difference.
+
+TODO: we might want to consider embedding the smaller tensor into the larger space and then compute the difference
+=#
+function _singular_value_distance((S₁, S₂))
+    V₁ = space(S₁, 1)
+    V₂ = space(S₂, 1)
+    if V₁ == V₂
+        return norm(S₁ - S₂)
+    else
+        V = infimum(V₁, V₂)
+        e1 = isometry(V₁, V)
+        e2 = isometry(V₂, V)
+        return norm(e1' * S₁ * e1 - e2' * S₂ * e2)
+    end
+end
+
 function calc_convergence(envs, CSold, TSold)
     CSnew = map(x -> tsvd(x; alg=TensorKit.SVD())[2], envs.corners)
-    ΔCS = maximum(zip(CSold, CSnew)) do (c_old, c_new)
-        # only compute the difference on the smallest part of the spaces
-        smallest = infimum(MPSKit._firstspace(c_old), MPSKit._firstspace(c_new))
-        e_old = isometry(MPSKit._firstspace(c_old), smallest)
-        e_new = isometry(MPSKit._firstspace(c_new), smallest)
-        return norm(e_new' * c_new * e_new - e_old' * c_old * e_old)
-    end
+    ΔCS = maximum(_singular_value_distance, zip(CSold, CSnew))
 
     TSnew = map(x -> tsvd(x; alg=TensorKit.SVD())[2], envs.edges)
-    ΔTS = maximum(zip(TSold, TSnew)) do (t_old, t_new)
-        MPSKit._firstspace(t_old) == MPSKit._firstspace(t_new) ||
-            return scalartype(t_old)(Inf)
-        return norm(t_new - t_old)
-    end
+    ΔTS = maximum(_singular_value_distance, zip(TSold, TSnew))
 
     @debug "maxᵢ|Cⁿ⁺¹ - Cⁿ|ᵢ = $ΔCS   maxᵢ|Tⁿ⁺¹ - Tⁿ|ᵢ = $ΔTS"