diff --git a/docs/src/convergence.md b/docs/src/convergence.md
index e368c2e..25167c6 100644
--- a/docs/src/convergence.md
+++ b/docs/src/convergence.md
@@ -1,10 +1,9 @@
 # Convergence checks
 
-In this page we give some tips on how to obtain converged simulations. 
-
+In this section, we analyze the numerical accuracy of our simulations by outlining the necessary approximations and providing practical guidelines to ensure convergence of results.
 
 ## Chain length $N$
-During a numerical simulation, a truncation on the number of chain modes (and therefore chain length) will be introduced, in order to work with a chain of finite length instead of a semi-infinite one. This truncation on chain modes, let us say $N$, introduces a sampling on the modes in the original environment.
+During a numerical simulation, a truncation on the number of chain modes (and therefore chain length) will be introduced, in order to work with a chain of finite length instead of a semi-infinite one. This truncation on chain modes, let us say $N$, introduces a sampling on the modes in the original environment. 
 
 ## Local dimension $d$
-A second truncation has to be introduced on the local dimension $d$ of each tensor comprising the MPS that will be dynamically evolved. The local dimension coincides with the truncated number of Fock's states of the chain mode's Hilbert space: each site of the MPS, can be filled up by at most $d$ excitations. Since in this case the excitations are bosonic, the Pauli exclusion principle does not hold, and this number should in principle be infinite.
+Another critical truncation is imposed on the local dimension $d$ of each tensor in the MPS that undergoes dynamic evolution. The local dimension dd corresponds to the number of Fock states retained in the Hilbert space of each chain mode. Since harmonic oscillators are, in principle, infinite-dimensional systems, truncating their Hilbert space to a finite $d$ is necessary for numerical computations. The choice of dd determines the maximum number of excitations per site in the MPS and must be carefully tuned to capture the relevant physics while ensuring numerical convergence.