How shall I address the complexity of maintaining randomly chosen groups across time-lagged survey?

In your first survey use Randomizers to set embedded data fields for three groups (e.g., group1, group2, group3). Use branches inside the 2nd and 3rd randomizers so you don't assign duplicate groups. You can the pipe the groups into your questions. Also in the first survey, update your contact list (or create a contact list) using a Contract Action or Trigger and save the groups as embedded data fields in the contact list.
In the 2nd and 3rd surveys populate the group embedded data fields from the contact list either through email invites, personal links or an authenticator. Pipe the fields as needed.

Dear Tom G
Thank you so much for your explanations. I have not used the functions that you mentioned in your explanations (e.g., piping the groups into questions, using contact list, etc.). Indeed, my Qualtrics knowledge is at the basic level such that I have used only basic randomizer and branch functions in the survey flow.
First, I didn’t quite understand “how to use randomizers to set embedded data fields for three groups”. You mean, I make a randomizer and then put set embedded data as below?
Second, from your explanations, it seems that I need the 2nd and 3rd randomizers and use branches so that I may not assign duplicate groups. I was not quite sure about where I should make randomizers. Should I make randomizers at an equal level? How specifically shall I use branch function to avoid potential duplication? Finally, I tried to pipe in the text from the embedded field. But, in the embedded field, there are to be many groups (e.g., group1, group 2, etc.) So, I am not sure about how I make them to be randomly assigned and then consistently appear throughout the surveys at different time points.
From my response, you may clearly see that I lack the basic knowledge of the Qualtrics. I admit that my understanding is at the basic level. I just do not know where to start and how to make it work. So, could you kindly explain the procedures that you suggested for me in more detail? Also, it would be very grateful if you could share with me some useful resources that may help me understand your suggested procedures and build the survey accordingly. My email address is usun2@uic.edu. If you could spare some time for me and show me how to do this with Zoom, it would be really grateful. Once again, thank you so much for your explanations. 

Your randomizers would be something like:
Randomizer (display 1 of 20, Evenly present)
Embedded data: group1 = people with bipolar disorder
Embedded data: group1 = blah blah blah
...etc...
Randomizer (display 1 of 20, Evenly present)
Branch: If group1 Not equal to people with bipolar disorder
Embedded data: group2 = people with bipolar disorder
Branch: If group1 Not equal to blah blah blah
Embedded data: group2 = blah blah blah
...etc...
Randomizer (display 1 of 20, Evenly present)
Branch: If group1 Not equal to people with bipolar disorder
AND group2 Not equal to people with bipolar disorder
Embedded data: group3 = people with bipolar disorder
...etc...
Then pipe ${e://Field/group1} or ${e://Field/group2} or ${e://Field/group3} into your questions as needed.
P.S. Emails don't show up in Community posts.

Dear TomG
Thank you so much for your kind explanations. Now I see how randomization and piping works. I never used embedded data before. It indeed is very powerful.
Could you give me some more explanations about how I pipe the embedded data from the 1st survey to the 2nd survey? It seems like I need to use contact list, which contains participant’s email address. However, we are going to use Prolific, which provides us Prolific ID, instead of participants’ email addresses. Further, when we conduct a longitudinal study on Prolific, it is not Qualtrics but Prolific that sends emails to participants (we do this by using Prolific ID). Does your suggested method also work with Prolific, too? As I am really a novice at using Qualtrics, it would be grateful if you could provide detailed explanations.
Once again, thank you so much for your kind explanation. It really is a great help to me.

Dear TomG,
Thank you so much for all your kind and detailed explanations. I really appreciate it. I may ask several other questions as I work on making the survey. Once again, thank you so much.