The phrase "a deep rift between" is correct and usable in written English.
It can be used to describe a significant division or disagreement between two parties, groups, or individuals.
Example: "There has been a deep rift between the two factions since the controversial decision was made."
Alternatives: "a significant divide between" or "a major split between".
It marked the official healing of a deep rift between Qatar and its neighbours.
Mother and daughter later reconciled after the abandonment created a deep rift between the two.
And, most clearly, a deep rift between a coach and his star player that simply could not be reconciled.
The conversation, leaked to Haaretz, a liberal Israeli newspaper, and confirmed by Israeli and German officials, reveals a deep rift between Berlin and Jerusalem.
In January, politicians adopt a new constitution after two years of turmoil that exposed a deep rift between Ennahda and the secular opposition.
The case has left a deep rift between those in Georgian society who believe that Russian agents have infiltrated the closest governmental circles and those who believe that innocent people have become entangled in Georgia's claims against Russia.
Some expressed concern that the obvious tensions between Mr. Gore and Mr. Clinton during the campaign -- and in the immediate aftermath of the election -- had solidified into a deeper rift between their followers that could hover over the party for years.
Even after a deep rift developed between the two men in 2011, Khamenei continued supporting Ahmadinejad's nuclear policy.
In countries like Pakistan, India, Bangladesh and Brazil, there is also a deep rift in trust between the social sector and the government.
The episode led some of the restrictions on imports to Gaza to be relaxed, but also caused a deep rift in relations between Israel and Turkey, which has indicted four Israelis for their roles.
A solution in Cyprus would end a deep rift within NATO between Turkey and Greece, both members, and open the way to the development of large gas reserves in the eastern Mediterranean that could upset the grip of Gazprom, Russia's state-controlled energy giant, on the Turkish market.
