I would not think of this story primarily as being about the heart in conflict with itself, but to the degree that this description applies, it applies to Emily and her beloved. On one hand, she must love him. She sleeps with him forever, and keeps mementoes of their love at hand. On the other hand, she kills him. Now, you could say she kills him to keep him close, and you would have identified the ways Emily's heart pulls her in two different ways: death and life, love and revenge, etc.