break away [phrasal verb] 1 : to get away from someone or something especially by using force or effort ▪ Large pieces of the rock ledge have broken away. [=broken free] —usually + from ▪ He broke away [=broke free/loose] from his captors and escaped. ▪ She broke away [=pulled away] from the other runners to win the race. —often used figuratively ▪ The company has broken away from the competition. ▪ young people breaking away from traditional values
2 : to separate or become separate from a larger group, country, etc. ▪ Three members of the band broke away and formed their own group. —usually + from ▪ a faction that has broken away from the main political party —see also breakaway
The second definition is what you need. As you see it is different from "break up".
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