When user opens the UI in new tab, new UI instance will be created. So they does not share the same state. Anyway the two UI instances share the same VaadinSession so you could use that. Save the login information to the session. When you init() the UI, check if the user is already logged in. If not redirect to login page, otherwise show your application. There is an example about this in wiki:
https://vaadin.com/wiki/-/wiki/Main/Creating%20a%20simple%20login%20view