I lost trust in my partner and it gives me a constant anxiety - is there a healthy way to change this?

Bonnie, thank you for reaching out and asking for guidance.  I see that your byline states that you "lost trust" in your partner which is giving you constant anxiety and you're looking for a healthy way to address this.  A small disclaimer before I go into my response: my response will be a bit on the general side seeing that the information you provided wasn't specific.  However, it is my hope that the questions and statements I pose will be a jumping off point to breaking the cycle you referenced above.

First off, I want to touch upon your last sentence where you stated that you "can't stop having anxiety around this situation without having black and white evidence that he has been fully honest"...have you attempted to speak to your partner about why his actions have broken your trust?  I know it seems things would be easier if it were so clear cut black or white, but unfortunately life is not like that.  There are many nuances to situations where it is not as simple as black or white.  This is called absolute thinking, which can skew our thought processes leading to actions that we may not be proud of.  And in your case, it was going through his phone.  The reason why I ask if you have attempted to talk to him about this is so you can explain to him where you're coming from, while also giving him the opportunity to explain his side of things.  Just how you alluded to your insecurities, it is very possible that your partner has insecurities of his own, which were exacerbating his?  

Using strategies to help with resolving this conflict will in turn help break this cycle.  Not knowing your interactions at the moment, it may be best to establish rules.  You can first start off by saying that you want to speak with him about what happened and that you want to have a productive conversation about how to move forward.  The first rule that I would put in place is that when each of you are speaking, the other person is quiet.  Doing this will help in making sure that you are hearing the other person.  Another rule to institute is "no blaming" language.  Meaning that when it is your turn to speak, you talk solely about how you feel and not pointing blame at the other.  Attached is a worksheet that does a good job explaining this in further detail - https://therapistaid.com/therapy-article/fair-fighting-rules-article 

Something for you to think about prior to going into this conversation is what do you think your partner will need to do to earn your trust back?  Thinking about this ahead of time will also help in guiding the dialogue.

Moving away from this conversation for a moment - how do you currently cope when you are feeling anxious?  Is there anything you do that helps you feel better, if even in the moment? Are you able to reach out to a friend?  Is there a certain type of activity you enjoy doing?

While you didn't go into detail about what the situation was that led to your partner breaking your trust, it does sound like you could benefit from talking to a licensed professional who can help you unpack this more.  If this particular instance opened up old wounds that maybe never healed?  I do think that the suggestions I made above could be a good start for you to change this in a healthy way.  Good luck and happy holidays.