Cornering gapless quantum states via their torus entanglement

Understand

The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter.

• We analyze the universal part of the EE for gapless systems put on tori in 2d/3d, denoted by $\chi$.
• Focusing on scale invariant systems, we derive general non-perturbative properties for the shape dependence of $\chi$, and reveal surprising relations to the EE associated with corners in the entangling surface.
• We obtain closed-form expressions for $\chi$ in 2d/3d within a model that arises in the study of conformal field theories (CFTs), and use them to obtain ansatzes without fitting parameters for the 2d/3d free boson CFTs.