He left because he was sent to an asylum.
He was one of Gormogon's (the cannibal that was making a human skeleton out of his victims) apprentice's. Zach blew up the lab doing an experiment, knowing that he would harm himself. He timed it too late and permanent damage was done to his hands. He was sent to hospital. After Booth and Bones do some investigating, Bones figures out it was Zach who had been helping Gormogon. Zach confesses that he murdered a man and was told he could go to prison or an asylum. He goes to the asylum.
In a later episode, Hodgins gives Zach a case file and Zach escapes. It seems he was able to do this for a long time. Zach returns to the lab to help the "squints" solve a case and then returns to the asylum. He then tells Sweets that he never actually murdered a man. Sweets tells him that he's going to tell the others but Zach warns him of that he would be in breach of his contract thingie and sweets can't tell anyone.
We are not sure yet if Zach ever comes back, but it doesn't say that he never returns. He could return and I hope he does! Hope I helped!
The episode when Zach leaves is the last in Season 3 called "The Pain In The Heart"
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In the season 3 finale, he is found to be Gormagons apprentice. He never killed anyone as mentioned later, but he does blame himself. He is currently institutionalized in a psychiatric facility. He doesn't make many appearances
The actor who played Zac didn't leave. The character Zack was involved with a cannabalistic serial killer, and because of this, he was sent to a mental institution, where the members of the Jeffersonian are still allowed to visit him, and occasionally let him help with cases. Hope this helps :)
Zachary ñZackî Addy is a fictional character from the television shows Bones. The actor that portrays Zack Addy is names Eric Millegan. This character is no longer a regular on the show.
His name is Zach Gilford and I believe he is currently on Friday Night Lights.
Zach Rosenblatt
it was Dr. John "JD" Dorian.
Alicia Favela.