May one answer amen while one is in the midst of bentching, when the one leading the bentching recites out loud in yaalehv’yavo, ‘zachreinul’tova…u’fakdeinivol’bracha….
We should not answer amein to the person saying yaaleh v’yavo loudly. The reason is since we are not allowed to talk while we are bentching, the same way we cannot talk out during Shemona Esrei, even to answer to kaddish or kiddusha, according to many poskim. After finishing the forth bracha one may answer amein to “zacreinu…”
Efrayim 1-148, R’ S. Z. Auerbach zt”l in Shmiras Shabbos Khilchoso correction to comment in chap. 57-1, that there is no obligation to answer amen to what is said in yaaleh vyavo, therefore we may not answer to it in middle of bentching because it will be a hefsek. Piskei Yeshuvos 183-16.