Adverbs that don't use 地
地 only CHANGES ADJECTIVES to adverb. Any adverbs without being conjugated from adjectives can exist without 地.


地 is commonly omitted. This happens usually when the adjective has ONE CHARACTER only. For example: 慢慢走 or 慢走. 地 is omitted since 慢 has only ONE character. The repetition of 慢 here is only for the purpose of expressing the action in a more visualized or vivid way.
兴奋 has two characters, and you cannot shorten it to one character to have the same meaning, so we usually don't omit 地 in this case.