Is there an authentic Hadith that states that a woman who leaves her home with her head uncovered is an adulteress and her husband is an adulterer, and what is the correct legal text for the ruling on one who does that?

No hadith has been found to support what the questioner mentioned, but it has been established in Islamic law that women are prohibited from going out displaying their adornments (tabarruj). This is supported by evidence from the Quran and Sunnah, including His —the Almighty— saying: (وَقَرْنَ فِي بُيُوتِكُنَّ وَلَا تَبَرَّجْنَ تَبَرُّجَ الْجَاهِلِيَّةِ الْأُولَى) "And stay in your houses, and do not display yourselves as [was] the display of [the former] times of ignorance." and His —the Almighty— saying: (وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنْهَا) "and not expose their adornment except that which [necessarily] appears thereof". And the Prophet’s —peace and blessings be upon him— saying: "The worst of your women are the mutabarrijat (those who display their adornments) and the mutakhayilat (the arrogant), and they are the hypocrites. None of them will enter Paradise except like a white-footed crow." It is also established that a husband is warned against condoning his wife's tabarruj, and he is labeled a dayyuth (pimp/cuckold).