diff --git a/docs/src/faq/DMRG.md b/docs/src/faq/DMRG.md
index 191c5ef211..c580829323 100644
--- a/docs/src/faq/DMRG.md
+++ b/docs/src/faq/DMRG.md
@@ -28,6 +28,7 @@ We list some of these with the most fundamental and important ones first:
   If 10 sweeps made a difference, try 20 sweeps.
 
 * Try setting the `eigsolve_krylovdim` keyword argument to a higher value (the default is 3).
+  This can be particularily helpful when the Hamiltonian is close to a critical point.
   This may make slowly-converging calculations converge in fewer sweeps, but setting it 
   too high can make each sweep run slowly.
 
diff --git a/src/mps/dmrg.jl b/src/mps/dmrg.jl
index cd85d488f6..e979b8bce8 100644
--- a/src/mps/dmrg.jl
+++ b/src/mps/dmrg.jl
@@ -126,7 +126,7 @@ Optional keyword arguments:
      or threshold to use for truncating the bond dimension or rank of the MPS.
   - `eigsolve_krylovdim::Int = 3` - maximum dimension of Krylov space used to
      locally solve the eigenvalue problem. Try setting to a higher value if
-     convergence is slow. [^krylovkit]
+     convergence is slow or the Hamiltonian is close to a critical point. [^krylovkit]
   - `eigsolve_tol::Number = 1e-14` - Krylov eigensolver tolerance. [^krylovkit]
   - `eigsolve_maxiter::Int = 1` - number of times the Krylov subspace can be
      rebuilt. [^krylovkit]