title: Cornering Gapless Quantum States via Their Torus Entanglement.
abstract: 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 on tori in 2D and 3D, denoted by χ. Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of χ and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for χ in 2D and 3D within a model that arises in the study of conformal field theories (CFTs), and we use them to obtain Ansätze without fitting parameters for the 2D and 3D free boson CFTs. Our numerical lattice calculations show that the Ansätze are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g., Kitaev's honeycomb model.
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.|Département de physique, Université de Montréal, Montréal, Québec H3C 3J7, Canada.
authors.forename: William
authors.initials: W
authors.lastname: Witczak-Krempa
authors.affiliation: Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Lauren E
authors.initials: LE
authors.lastname: Hayward Sierens
authors.affiliation: Department of Physics and Astronomy, University of Waterloo, Ontario N2L 3G1, Canada.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.
authors.forename: Roger G
authors.initials: RG
authors.lastname: Melko