I did my PhD 4 years ago. I was not comfortable with my guide but I concentrated on my work, and I successfully completed the PhD. But I published a little work with his name as correspondence author. But now I am in good position in another country, so I need to publish my PhD work without his name as co-author. If I publish a paper of my PhD work without my supervisor's name, what will be happen? Are there any legal problems that will be raised?
You have left at least two important things unanswered:
Has your supervisor contributed to your work? (How contribution is measured depends on the field you are working in, it could be through "real" intellectual contribution, feedback, funding, ...)
But now I am in good position in another country so I need to publish my PhD work without his name as co author.
Why do you need to publish without his name as a co-author?
If I publish a paper of my PhD work without my supervisor name, what will be happen? Is there any legal problems will raised?
If he has contributed to your work, there may be several legal problems such as fraud or copyright infringement.
If you are sure that he has not contributed in any way to your thesis (which is unlikely) then you are fine to publish on your own. Otherwise you should talk to him and ask him if he thinks he has made a significant contribution and wants to be your co-author.
If you have discussed the paper with your supervisor in the past years; then your publication should meet his rights on the paper as he has previously contributed to your paper. Furthermore, if your research paper is done under financial support of your PhD university; then you have to acknowledge their rights too.
I think that the contribution of a co-author to a paper is important in acknowledging their right in project or paper, their supervision to your PhD thesis does not bring any right to your further (after graduation) academic publications.
As an instance, a paper is written based on a supervisor's contribution to it and it is part of a chapter of your PhD thesis; so it is obvious that you have to contact him about your paper. But if after graduation in the recent years you have found a good idea and worked on it without help of nobody else so there is no need to talk about your paper with others.
As a general rule, if you have never discussed your research project or paper with your supervisor, he has never contributed to your paper, you never used his resources, your PhD university does not hold any right to your paper idea and you meet the rights of financial supporter of your paper; then you may publish your paper solely. Otherwise, you have to meet their rights in your publication. Also, please note that one may build his academic relationship based on this rule to the other colleagues or students too. If and only if they have contributed to your paper, they can be a co-author of that paper.
I understand that you are a better researcher after a few years but I think that talking to a senior researcher and professor and asking him to read your paper will allow you to find your mistakes and publish better papers. Also, working with other researchers will add to your reputations and build connections with them. They may also contribute their papers with you and may ask you to read their papers in future.
This question has good answers to this question: Advisor's/University's rights in the PhD/MSc alumni's research projects and publications
Your new paper is based on your previous work, so if he has helped you in this new paper then give him credit. But it seems that this new paper is strictly your work, and no credit would be due. BUT you will be referring to a previous work which he supervised. Your PhD is your original research under his supervision. Unless he physically wrote words in your paper, either your new work or your PhD, I wouldnt think its necessary to credit them.