Cubism arose during the early 1900s. It was led mainly by painters like Pablo Picasso and Georges Braque. A main characteristic of Cubism is the emphasis of a subjective mental experience over previous periods' objective logical experience. There is also a lot more fragmentation of thinking.
In literature that sentimentality expresses itself with stream of consciousness writing and/or writing a story from multiple perspectives. William Faulkner's novel As I Lay Dying, for example, tells the story from about 15 different perspectives. Each character is given his or her own voice and vocabulary which causes the narrative to be told in very distinct ways.
Perhaps a contributing factor to Cubism's concern with and emphasis on the internal mind is the work of Sigmund Freud whose psychoanalysis is very much focused on the internal struggles of the mind and much less so on outside influences. Freud himself even divided up the human psyche into multiple parts: the id, the ego, and the superego.