They are both correct, though each is more common in a different region.
My understanding is that AmE treats "summer break" as an abstract, as it's the name of a period that happens every year. In this interpretation, "summer break" is a general concept, it's not just a specific break during the summer of a specific year.
Therefore, it is treated the same way as other abstract nouns and it receives no article. Other examples include:
Love is all around us.
I wash myself using water.
Detail is not something I concern myself with.
All of these nouns refer to general concepts, not concrete instances, hence why they're abstract.
"The summer break" is more common in BrE, and it tends to refer to a specific break during a specific summer (which is usually contextually obvious).
This makes it a concrete noun, which does receive an article. Note that I am using the same nouns as before in this example, but their meaning has slightly shifted from before.
The love I get from my family is amazing.
I dipped my toes in the water.
Just look at the details in this painting, it's breathtaking.
This is talking about specific instances, not general concepts. The specific instance of love from my family (not all love), the specific body of water (not all water), the specific details in this painting (not any unspecified details).
Theoretically, you'd be talking about every summer break when you omitted the article, since you're referring to the abstract concept. However, casual speech is not as strict about rules, and it's generally understood that even though it may be used as an abstract noun, it can make sense to only refer to the summer break which is contextually relevant.