Job search advice for possible PhD dropout
Based on my own experience outside of academia, the problem right now is that all of the reasons you've stated are negative against your current situation; you haven't said anything positive about why you want a job as an analyst (or whatever other job you might seek out), just that you don't want to continue in your current position.
I've found the best results come from flipping around what you don't want, and using it to be clear - both to yourself and to people you want to work with - what you do want, and thus why you are a good fit for the position.
Let's say you have the personal position, "my research is meaningless, it will be of no practical use to anyone ever" (a version of cynicism about your research - adjust to suit your real feelings). You can flip this around to stating a positive: you want to use the skills and knowledge you've gained to be of practical value to business. You thought academia was the way to do that when you were [an undergrad, changing fields, your story goes here], but now that you've begun to explore opportunities in industry, there are ways of contributing that are a better fit for you.
In terms of burnout, I don't know how to package that in a good way, because it is just as big of an occurrence outside academia as within it. Setting limits, building a balanced life, and ensuring regular rest and rejuvenation is not something that is automatic anywhere. Some companies tell a good story about how it is important to them, but for most places its a marketing line. There is always someone willing to take advantage of anyone that doesn't have strong personal boundaries and a willingness to say no. However, there are many businesses where the "norm" is a healthy schedule, so you may prefer that to a place where everyone is stressed to the max all the time. You can tacitly inquire about "work-life balance", or what the "typical work week and schedule is like" in that department.
As scaahu suggested, it is usually OK to just come out and say that you are looking for better pay. You can choose to give a reason, such as wanting to contribute to help family members who are having a rough time (or ill, etc), but everyone knows graduate students have to live pretty thin compared to full-time professional employment in industries like finance or tech, so you usually don't need to. People in such industries are often quite proud of their pay, so they don't really blame people for wanting in; however, this is in no way establishing a very good fit for a position, because of course you want more money.
In summary, you need to come up with a compelling - and short - story to tell about how you are a good fit for the position you are seeking. Then, with a positive way of saying what you want, leaving your current position is just a question of seeking a better fit. Talk about how you are running towards something you want - not running away from something you don't want - and most importantly, how you can be of value in the new position.
For the final question of whether or not to put it in the cover letter, there is no universal answer for this. If you put it in a positive way that talks about how you are interested in moving from your current position into the new position, that's usually OK, as it makes it clear you are planning to side-line or drop the PhD program. Some advocate for just saying only how you are qualified and potentially valuable to the company, and leave all questions about why you want to transition and what you are going to do about your current job/program for the interview. You can do either. If you find it easier to describe - one approximately 1 sentence, maybe 2 at most - a positive way to say how you are planning to leave your current position and dedicate yourself full-time to the job, then go for it. Have others read it and if it comes off in the least bit defensive or negative, cut it and practice your in-person delivery.
Way too many personal details may look unprofessional. You might try something like
I was not satisfied with my progress in academia, and I do not want to lose any more time by trying. I believe I can fully utilize my productivity and develop myself better in the industry, by the help of financial means.
This is both honest, motivational, and looks less pretextish. Not everyone will care about what you lived in your personal life.
Making the decision to leave academia can be difficult, so congrats on knowing what you want!
I think one of the simplest solutions to explaining your situation to potential employers in industry is that after you worked on your PhD for some time you realized that you rather work in a position in your field that is more hands-on and less research, focused. You also can say that you prefer the culture of working in industry (set hours, solid deadlines, little need for securing grants for research, etc.). This is more professional, but still potentially related to the reasons you would like to leave academia.
One question - if you are sure that you want to leave academia, why consider finishing your PhD? It seems like your time and effort would be best used focusing on your career. Not finishing your PhD is not a failure - you changed your career goals. I have seen a number of colleagues who worked through their PhD only to take jobs outside of academia (where they didn't need the PhD) and they felt like they saved their time and money. Just a thought. Good luck!
Sample cover letter:
In May I will complete my nth (third, e.g.) year of graduate studies in (name of field or department) at (name of University). Having (list some specific accomplishments), I feel ready to apply my modeling and computational skills in the real world. My target job is bla bla.
If you are asked why you're not staying to complete your PhD:
I feel well prepared to work in (name of field). (You could talk up a project you recently completed at this point, or just leave it as is, short and sweet.)
(The potential employer does not need to know that you did the smart thing and arranged for a leave of absence, so as to avoid burning your bridges with your department.)
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Betterthan Kwora 17 days
I am considering dropping out of my PhD program, which I am halfway through (pre-proposal), and am applying to full-time jobs. My plan is to go on a leave-of-absence for a year, and afterwards either return and finish my PhD, or quit my program permanently. Even if I finish my PhD, I plan to leave academia, most likely for finance. I'm applying primarily to quantitative analyst positions to give myself a better idea of whether I want this as a long-term career. And, if I get a job and still enjoy it after a year, I plan to formalize my PhD dropout status.
I have a solid publication record in a very relevant area, so my research skill is an important part of how I'm selling myself. But I don't know how to discuss my current situation in my cover letters and interviews. The honest answer is a combination of burnout, personal/family circumstances, and cynicism over my research. But is saying this unprofessional? Also, should I leave out all discussion of my situation in my cover letters, and just wait for interviewers bring it up?
Nobody about 5 yearsburnout, personal/family circumstances, and cynicism over my research None of these would help you to land a job in industry because you could have them when you work on an industry job.
Betterthan Kwora about 5 years@scaaahu Right, so how do I explain my decision?
Nobody about 5 years"I want more money" would be an honest and good one.
Patricia Shanahan about 5 yearsI am a little troubled by the leave-of-absence idea. Either an industry career or a PhD program is more likely to be successful if pursued with determination and commitment.
aparente001 about 5 years@PatriciaShanahan - Note, OP does not need to tell the potential employers that a leave of absence was requested/granted.
Patricia Shanahan about 5 years@aparente001 I know. I am concerned that the OP may end up never really committing to industry or academia, or at least not for many years.
Betterthan Kwora about 5 years@PatriciaShanahan In my department, leave has a hard 1-year limit for PhD students. And I'm definitely leaving academia; I'd just consider finishing my PhD if I get the sense that it would significantly limit my career progression in quant finance.
owjburnham almost 5 yearsCould you please specify the country in the title/description/tags?