Should one avoid sleeping during the day?[1]
If one needs to sleep during the day in order to have strength to learn Torah then he may do so. However he may not sleep for a long time as it is forbidden to sleep during the day for a period of over 60 breaths.[2] [Nevertheless if one needs to sleep more than this amount in order to have strength to serve Hashem then he may do so[3], and so is the custom of Tzaddikim and Gedolei Yisrael.[4]]
On Shabbos: On Shabbos it is a Mitzvah to sleep during the afternoon if he is accustomed to sleep during the afternoons of the week.[5] [Furthermore based on Kabala it is a Mitzvah to always sleep for some time on Shabbos afternoon and so was the custom of the Arizal.[6]]
[1] Michaber 331:1; See Sefer Shemiras Haguf Vihanefesh [Lerner] 54:19
[2] According to Kabala one who sleeps during the day loses the Ibur of the soul of Tzaddik that was in him. [Kaf Hachaim 231:5-6]
[3] Shulchan Hatahor 231:1; Binyan Olam 1; Kaf Hachaim 231:6; Piskeiy Teshuvos 231:1; To note from Michaber 4:15 which does not mention any prohibition in sleeping during the day. This is more explicitly mentioned in Admur 4:15 which writes the law of washing regarding one who sleeps 60 breaths during the day. Likewise in Admur 190:2 and Rama 190:1 they rule that one is to sleep on Shabbos afternoon if he is accustomed to sleep during the weekday afternoons. Hence it is clear that Admur does not hold that sleeping 60 breaths during the day is a standard prohibition as is implied from Michaber above. Vetzaruch Iyun as to whether Admur completely disagrees with the prohibition or simply learns that in many instances it does not apply.
[4] Aruch Hashulchan 231:1; Darkei Chaim Veshalom 320 slept for about one hour during the day.
[5] 290:2; Rama 290:1
[6] Shaar Hakavanos 74; Emek Hamelech Hakdama 3:2; Siddur Haarizal; Siddur Kol Yaakov; Kaf Hachaim 231:5; Lekutei Torah Vieschanan “Biur” P. 6; Likkutei Sichos 12 p. 254 footnote 50; However see Kitzur Dinei Shabbos Miluim p. 87 states that nevertheless Chassidei Chabad were particular not to sleep on Shabbos.