From 963543aacbb994f76fe8a614ca1de5b49a5a3709 Mon Sep 17 00:00:00 2001
From: Angela Riva <62027430+angelariva@users.noreply.github.com>
Date: Mon, 25 Nov 2024 13:55:07 +0100
Subject: [PATCH] Update convergence.md

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 docs/src/convergence.md | 9 +++++++++
 1 file changed, 9 insertions(+)

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+# Convergence checks
 
+In this page we give some tips on how to obtain converged simulations. 
+
+
+## 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.
+
+## 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.