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 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. Our numerical lattice calculations show that the ansatzes 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.

4+7 pages, 4+4 figures. v3: improvements throughout to improve clarity; Appendices have been expanded

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Cited by in corpus (16)

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• Generalizing the entanglement entropy of singular regions in conformal field theories
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Holographic entanglement entropy for perturbative higher-curvature gravities
• Holographic torus entanglement and its RG flow
• Cubic trihedral corner entanglement for a free scalar
• Conformal bounds in three dimensions from entanglement entropy
• Aspects of N-partite information in conformal field theories
• Probing trihedral corner entanglement for Dirac fermions
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• Disks globally maximize the entanglement entropy in $2+1$ dimensions