Updated March 2, 2023: They published one book that I could find last year and their last tweet is over a year old. I would not approach them with a submission at this time.
Harvard Square Editions is a publishing company founded by a group of Harvard Alumni. They accept novel and novella submissions with environmental and social themes. HSE seeks work of the highest literary quality.
Despite being a very small publisher with a very small budget, books they have published have won a variety of awards and honors, including the National Book Awards 5 under 35 Award in 2016. They have also been talked about in various established publications, including The Guardian.
They do not offer advances but they focus on in-depth editorial work and they seem to be getting pretty good at promoting the books they publish. Unlike many publishers they do not focus primarily on publishing literary fiction by north American authors. They have published books by authors hailing from all over the globe.
Publishers Weekly wrote an article about Harvard Square Editions in 2011 that contains some interesting information, that you can read here.
To read their brief submission guidelines or to submit using their online form go here. To get a better idea for what they have previously published go here.