No, there should not be a second referendum. The House of Commons as our national parliament should be asked to vote what to do (if anything) about the result of the referendum, the results of which were never legally binding on our government to implement, even if you accept that the simplistic wording of the question allowed no interpretation of what an alternative to the current arrangements might be. This should satisfy the Brexiteers so concerned about national sovereignty all the time and could mean, if a bit of backbone was shown by the Labour Party especially, that the disastrous (I don't exaggerate) and self-inflicted chaos to come could just be avoided.
If you think these are just the ravings of a Remain supporter, I would counter that in the Sunday Telegraph last week a journalist by the name of Tim Ross, obviously thinking Remain were going to 'win' the argument, expressed the opinion that nothing other than a 60/40 vote in favour of Remain would put the matter to bed. Given the constitutional and administrative changes required to implement a withdrawal by the UK from the EEC, it is ludicrous to suggest that it happen on a straight 50% plus one vote from those who could be bothered to turn out.